$A$ and $B$ are square complex matrices of the same size and $\text{rank}(AB − BA) = 1.$ Show that $(AB − BA)^2= 0.$
On the nilpotence of the matrix $AB-BA$
How to download packages from a command-line given repository? It is not about the common download &amp; install thing, what apt (aptitude, etc) does, it is a scripted download a package file.  I found the dget tool for this task, which works quite well. But, unfortunately, it doesn't have any option to specify a different repository URL as it is given in the /etc/apt/sources.list.  Is it somehow possible? Actually, a dget-like functionality would be the best, but where I can also specify the repo URL.    P.s. thank you very much the scripts, but I would like to prefer a debian tool for this very simple task. It will be part of a buildscript, for external usage, and any unneeded complexity has intolerable collateral costs. It must be done by a debian tool.  P.s.2. Finally I solved this with updating the system-wide repos, and downloading the packages with dget. Thank you very much the scripts! I have used the websites of SO a lot the past few months because I am busy with a large scale web project. I feel I get better answers here on SO than when I just do a Google search, maybe because I can be more specific here with my problem, and the responses are really fast.  Occasionally when I am not working I try to answer some questions, but the question almost always has an answer which is 'as good as' or 'better' than the answer I would supply.  So my question/answer ratio is about 20/1 something, if not more. When I look at my profile page I see a bucket-load of questions and almost nothing I answered myself.  Is this considered bad behaviour? I can see that this looks a little egoistic.  : One devoted to one's own interests and advancement. Double value returns 0 Here's an example:  Double d = (1/3); System.out.println(d);   This returns 0, not 0.33333... as it should.  Does anyone know? Is it possible for an iPad to get a virus? I am not able to find an answer to the following question:     For which positive even integers $k$ is the integer   $$p^2+k$$ prime, where $p$ is a prime number $\gt5$? How to use a field value in Template.php How to modify an invalid '/etc/sudoers' file? How do I edit an invalid sudoers file? It throws the below error and it's not allowing me to edit again to fix it.  Here is what happens:  $ sudo visudo &gt;&gt;&gt; /etc/sudoers: syntax error near line 28 &lt;&lt;&lt; sudo: parse error in /etc/sudoers near line 28 sudo: no valid sudoers sources found, quitting How do I parse command line arguments in Bash? Say, I have a script that gets called with this line: ./myscript -vfd ./foo/bar/someFile -o /fizz/someOtherFile  or this one: ./myscript -v -f -d -o /fizz/someOtherFile ./foo/bar/someFile   What's the accepted way of parsing this such that in each case (or some combination of the two) $v, $f, and  $d will all be set to true and $outFile will be equal to /fizz/someOtherFile? How to enable multiple logon remote desktop in Windows 7 In contemporary American English usage, I come across sentences like:   I ain’t got no money.  Ain’t no man like him.    Saying ain’t no sounds incorrect to me because it is a double negative.  What is the origin of this particular construction? I wasn’t able to find anything online related to the origins of this incorrect usage. Where is the operator panel in Blender 2.8? The identity cannot be a commutator in a Banach algebra? The Wikipedia article on  claims, without a proof or reference, that there does not exist a (unital) Banach algebra $B$ and elements $x, y \in B$ such that $xy - yx = 1$. This is surprising to me, but maybe the proof is straightforward; anyone have a proof and/or a reference?   More generally, I would have naively thought that I could embed any ring into a Banach algebra. I guess there are actually serious restrictions to doing this; are these issues discussed anywhere? When I cut a layer using marquee tool, I get blur edges to cut side. How do I get sharp edges after cut? I am using rectangular marquee tool to cut a portion of the layer in photoshop cs5, but after cutting, the edges are not sharp, I get blur edges.      how can I get sharp edges? I've seen many boads with weird zig-zag shaped tracks just like the one below. Why are they designed like that? I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not &quot;The Word for World is Forest&quot;, nor &quot;Direction of the Road&quot; (from ), nor &quot;Vaster than Empires and More Slow&quot;, the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... Co-Buyer Automobile As a co-buyer on an automobile, can the other party take full possession? Both parties names are listed as the Purchaser's. Only one purchaser signed the retail order for the motor vehicle, and if so, how can one become a no co-buyer? How are virtual functions and vtable implemented? We all know what virtual functions are in C++, but how are they implemented at a deep level?  Can the vtable be modified or even directly accessed at runtime?  Does the vtable exist for all classes, or only those that have at least one virtual function?   Do abstract classes simply have a NULL for the function pointer of at least one entry?  Does having a single virtual function slow down the whole class? Or only the call to the function that is virtual?  And does the speed get affected if the virtual function is actually overwritten or not, or does this have no effect so long as it is virtual. how to launch Bluez on Lubuntu Trying to launch a BT adapter/manager(default installed on Lubu)a little window informs me that it cannot because there's no Bluez launched.  In terminal: sudo apt install bluez, it answers: Bluez is already the new version (5.46-0ubuntu3) Then invites me to remove a couple of obsolete packages.  So where's Bluez Daemon to launch?  Writing:systemctl status bluetooth.service ; hcitool dev  Answer:   bluetooth.service - Bluetooth service    Loaded: loaded (/lib/systemd/system/bluetooth.service; enabled; vendor preset    Active: inactive (dead)      Docs: man:bluetoothd(8)   Command:lspci -k | grep -A3 -i "wireless\|network\|bluetooth" Answer: 04:00.0 Ethernet controller: Qualcomm Atheros AR242x / AR542x Wireless Network Adapter (PCI-Express) (rev 01)     Subsystem: Quanta Microsystems, Inc AR242x / AR542x Wireless Network Adapter (PCI-Express)     Kernel driver in use: ath5k     Kernel modules: ath5k 0f:06.0 CardBus bridge: Texas Instruments PCIxx12 Cardbus Controller oem@oem-Extensa-5220:~$ When updating I got this error message:  W:Failed to fetch cdrom://Ubuntu 11.10 _Oneiric Ocelot_ - Release amd64 (20111012)/dists/oneiric/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs W:Failed to fetch http://ppa.launchpad.net/synce/ubuntu/dists/your_ubuntu_version/main/source/Sources  404  Not Found   What to do? Too much memory getting used I have been feeling this way for a while, looking at task manager mentally ballparking how much physical memory should be in use, and noticing a large disparity. I finally got around to measuring it. Taking the results of tasklist and adding, gave about 3.87 GB. Task manager told me I was using 4.6 GB of memory. This seems like a large disparity. Where did it go?  EDIT: So its clear, it is not going to prefetch. It has also been suggested that its part of the OS, but not part of any of the system processes. If this is true, please find a way to get the OS to tell me how much memory is getting used. Since I want to find out where the memory went, asking me to look at the difference does nothing for me.  EDIT 2: It is not the following:   The kernel The cache Hardware reserved memory   Picture of resources taken up. Not quite sure what it will do but...