A matrix A is said to be invertible if there exists a matrix $A^{-1}$ such that $A\cdot A^{-1} = I$.  Given that we find a matrix (call it $A^{-1}$) such that $A\cdot A^{-1} = I$, I'm wondering why it is enough to stop here and not check whether $A^{-1}\cdot A = I$ as well. Any hints?
If $A$ and $B$ are square matrices such that $AB = I$, where $I$ is the identity matrix, show that $BA = I$.    I do not understand anything more than the following.   Elementary row operations. Linear dependence. Row reduced forms and their relations with the original matrix.   If the entries of the matrix are not from a mathematical structure which supports commutativity, what can we say about this problem?  P.S.: Please avoid using the transpose and/or inverse of a matrix.
Reference — What does this symbol mean in PHP? Is there any parameter (in terms of physical quantities such as mass, length, charge...) which can be used to decide when to treat a system quantum mechanically and not classically? In Unity3D, how do I create an efficient scratch card effect? I want to create a scratch-card-like effect in new Unity UI's new Image tag.  I know it's possible with setPixels, but that's prohibitively expensive on mobile devices.  Something like this:    I'd like the user to be able to drag on any part of the image to "scratch off" the top layer and reveal the content underneath it.  How can I do this? How should duplicate questions be handled? What should I do when I see a question that is a duplicate of another one?   Should I answer it? Should I downvote it? Should I comment? Should I edit the question to indicate it's a duplicate? If I can, should I (vote to) close the question? What happens when I vote to close as duplicate? Or: Why did a comment with my name on it just appear? Should I flag it for moderator attention? What about similar or related questions? Let: $P(x) = a_nx^n + a_{n-1}x^{n-1} + ..... + a_1x + a_0$ where $a_0a_n &lt; 0$ I have to prove that the Polynomial $P(x)$ has at least one positive root how can I prove it? Any ideas? I think I've got it down to the most basic case:  int main(int argc, char ** argv) {   int * arr;    foo(arr);   printf("car[3]=%d\n",arr[3]);   free (arr);   return 1; }  void foo(int * arr) {   arr = (int*) malloc( sizeof(int)*25 );   arr[3] = 69; }   The output is this:  &gt; ./a.out   car[3]=-1869558540  a.out(4100) malloc: *** error for object 0x8fe01037: Non-aligned pointer                          being freed  *** set a breakpoint in malloc_error_break to debug &gt;   If anyone can shed light on where my understanding is failing, it'd be greatly appreciated. Is there a point of beating Vault of Glass raid on Hard after finishing on Normal? Strange problem with BibTeX sorting Data defined label position for more than one scale in one layer I'm looking for a better labeling-solution for my projects. It seems to be difficult - but maybe I'm just blind?   My projects: I build  printed bike-hike-books. The main scale is 1:75k and there are a city scale of 10k and a overview scale of 200k. Because I like to have a "cartographic" quality of labels placements, I touch every single label and move it to it's best position. I have to do this for every single scale so my labeling columns for 3 scales look like this ('scale 1' stands for 10k 'scale 2' for 75k  and 'scale 3' for 200k):    But before I try to explain in detail, I build this simple Example-Project where you can see and test my (old) labeling solution for 3 scales:   Well, it is working but:    You need labeling columns for every scale  You need a layer for every scale   I'm looking for a much better solution without duplicate layers and tons of columns. I count on your creative minds!  EDIT: I added this two very dense map as examples:    There is only one single possible position for "St. Paulus Dom" and it's not any quadrant:   Every label has to be moved manually. Some of the labels are not in a quadrant. How does the Golden Ratio/Spiral Work? Is it useful with Logo Design? Getting inverse of a transposition key Locking a vehicle bicycle rack We are planning a trip with a bike rack attached to our trailer hitch. What is the best way to lock the bikes while the vehicle is unattended? I see some racks have locks on the knobs but they don't seem very strong.   What do you suggest? SimpleXML: Selecting Elements Which Have A Certain Attribute Value Is there an online community to find travel partners (for mountains, sightseeing etc.)? Is there an online community to find travel partners for mountain trekking or sightseeing, or anything else?  I don't want to travel to foreign mountains alone, but I don't know where to search for company. There's a great community for accommodation (I mean CouchSurfing) so I think there should be something in "reverse" direction (searching not the place to stay but the people to go with). Old phone cannot connect to computer, the "computer connection" icon appears on phone I would like to get some pictures and audio out of an AT&amp;T SGH-a687 phone onto my Mac computer. I first tried connecting it to a New PC Studio on a PC, but there was a problem after transfer 2 photos, so I tried again. But the PC could no longer detect the phone, even though the "connected to computer" icon appears on the phone. I tried a different cable, different USB ports. No use.  So I downloaded the Samsung Kies on my Mac. Same thing, it tries to search for the phone once I connect the phone, but the computer doesn't detect anything. The phone still shows the "connected to computer" icon.  There is also Bluetooth (no internet on the phone) on the phone, but it failed to send the picture each time I tried.  What can I do at this point? Please also suggest data extraction software for either Mac or PC, if that's the easier route. Today I found something strange on my newly installed Windows 7 OS - my "users" folder C:\Users was shared and "Everyone" had full access... I disabled that and now it seems fine, however I'm a bit scared actually, I'd like to know what caused that and if my system is compromised. Say that Player X is 2nd in the initiative. 1st is the Black Court vampire that is in a rage and taking a swing at Player X. Player X gets a built in defense [Athletics/Fists + 4dF] but can Player X instead use his action this turn to cast his Rote Evocation Shield?  It is not his turn in the initiative order. A Block is an Action that a Player can take on his turn.   Thematically though, it seems to make sense that the char could cast a Rote Evocation Shield in response to an attack ahead of him in the initiative order. At least thematically in the books. Also, the example in YS252, shows him reacting to an attack by Agatha Hagglethorn by bring up his shield.  I am hoping there is some as yet undiscovered dark corner where this concept is covered or squashed. I can't delete more than 5 of my own posts in a single day. Is this a bug, or intended behavior? I'm trying to clean up old, crappy posts of mine.    Similar-looking problem, but it claims to be : Change rep required to downvote on MSE To make your opinion known on MSE you need both up and downvotes. Given at the moment you need 125 rep to downvote on this site, the voting patterns will be skewed positive because not everyone is active on the site.   This is to be expected for regular Stack Exchange sites as you are expected to be involved in the community before you are deemed knowledgeable enough to be part of the community voice. However, MSE is different because you are voting for the entirety of the Stack Exchange network and you shouldn't need to be active on MSE itself to have a voice on changes to the entire network.  This is especially important for questions like  because it will effect every network to do with coding at all. This was brought up in .  I would suggest reducing the rep required to downvote on MSE down to 100 (or 101) rep. This is the amount you get for the site association bonus. This is given once you achieve 200 rep on any network site and shows that you are active in at least one community. I think this would be the perfect use of the association bonus in showing that you are a member of the Stack Exchange community. Can I pay two different costs with the same payment?