Given a matrix $A$ of rank $n$, show that $\det(\operatorname{adj}(A))=\det(A)^{n-1}$ and $\operatorname{adj}(\operatorname{adj}(A))=(\det A)^{n-2}A$
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
Modern movie where rich people can buy a personal assistant that sit in a small egg This is a modern movie and rich people can buy this egg with a personal assistant. It's an actual person in it (or a person's mind). I believe it can even operate a toaster.  I believe later in the movie, a person (or their mind) can be transferred to such an egg. As a punishment, they increase the speed of time inside that egg to make the person inside the egg bored to death, so to speak. Outlook from time to time makes an operation 'Send and Receive.' This can sometimes be quite slow and Outlook hangs while this is done.    Is is possible to set different intervals for different mail accounts (if user has multiple accounts configured within Outlook, e.g., main Exchange account and one or more IMAP accounts) If yes (or even if only for some [e.g., IMAP accounts], where in the settings it can be configured?  (e.g., Outlook 2007) What can I do if my USB flash drive is write-protected or read-only? Where to put the periods when using a parenthetical sentence? I have two complete sentences; the second is in parentheses, essentially a comment on the first.  Where do I place the periods?  I would use this:     They played opera. (I covered my ears.)   Is this punctuation correct? This is what I see:  GNU GRUB version 2.02~beta2-9ubuntu1  Minimal BASH-like line editing is supported. For the first word, TAB lists possible command completions. Anywhere else TAB lists possible device or file completions.  grub&gt; _   What should I do now? Prove that there are infinitely many primes and non-primes in the numbers $10^n+1$, where $n$ is a natural number. So numbers are 101, 1001, 10001 etc. Display current layout (language code/country flag) in keyboard indicator Just upgraded from 10.04 to 10.10, and the keyboard indicator applet no longer displays the two-letter country code for the active layout.  This is terrible. Is this the default behaviour? Anyone using two layouts can't tell which language they're in.  I can't seem to find the setting for this, it used to be in the preferences for keyboard layout.  Update 1: In case this wasn't obvious - I have two keyboard layouts - English and Hebrew. I just upgraded form 10.04, where the country code (USA/IL) was displayed, overlaid on the flag.  Now all I get is a vague keyboard icon, and can't find the settings for this.  Update 2: this seems to be a , and is now back in Maverick Same as title, want to kill alt-tab, etc. \bar vs. \overline - when to use what, semantically? Following the question "" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.  I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".  Then I just tried  \documentclass{article}  \begin{document}   \[ \bar{a} \overline{a} \]   \[ \bar{abc} \overline{abc} \] \end{document}   where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).  So, the question here is:  What does \bar represent semantically? And when to choose it over \overline and vice versa? an analytic function from unit disk to unit disk with two fixed point prove that if  $f:\mathbb{D}\rightarrow\mathbb{D}$ is analytic with two distinct fixed point then $f$ is identity. I thought if one of the fixed points was zero by schwarz lemma this statement is easily proved. but what can I do if fixed points were nonzero? What is the difference between a homepage link with or without a trailing slash? Determine when $\sum_1^\infty \frac{(2n)!x^n}{n(n!)^2}$ converges. By ratio test, when $|x|&lt;1/4$, the sum converges, $|x|&gt;1/4$ diverges. But I'm not sure about $|x|=1/4$. By Stirling's approximation $\frac{(2n)!(1/4)^n}{n(n!)^2}\sim\frac{4^n}{n{4^n}\sqrt{ \pi n}}\sim\frac{1}{\sqrt{\pi}n^{3/2}}$, so when $|x|=1/4$, the sum converges. But I haven't learned Stirling's approximation yet, so how to prove that when $|x|=1/4,$ the sum converges, without using it? How can I use multiple accounts with Telegram? Is there a way to have two copies of  app in Ubuntu each with a different account?  It seems copying the app in another folder does not work. Why doesn't my question show up? is invisible in the  section, but visible in the  section. What gives? I want to try to convert a string to a Guid, but I don't want to rely on catching exceptions (   for performance reasons - exceptions are expensive for usability reasons - the debugger pops up  for design reasons - the expected is not exceptional   In other words the code:  public static Boolean TryStrToGuid(String s, out Guid value) {     try     {         value = new Guid(s);         return true;     }     catch (FormatException)     {         value = Guid.Empty;         return false;     } }   is not suitable.  I would try using RegEx, but since the guid can be parenthesis wrapped, brace wrapped, none wrapped, makes it hard.   Additionally, I thought certain Guid values are invalid(?)    Update 1   had a good idea to catch only FormatException, rather than all. Changed the question's code sample to include suggestion.    Update 2  Why worry about thrown exceptions? Am I really expecting invalid GUIDs all that often?   The answer is yes. That is why I am using TryStrToGuid - I am expecting bad data.  Example 1 . I might be parsing folder names, checking to see if the text after the final . is a GUID.  c:\Program Files c:\Program Files.old c:\Users c:\Users.old c:\UserManager.{CE7F5AA5-6832-43FE-BAE1-80D14CD8F666} c:\Windows c:\Windows.old   Example 2 I might be running a heavily used web-server wants to check the validity of some posted back data. I don't want invalid data tying up resources 2-3 orders of magnitude higher than it needs to be.  Example 3 I might be parsing a search expression entered by a user.     If they enter GUID's I want to process them specially (such as specifically searching for that object, or highlight and format that specific search term in the response text.)    Update 3 - Performance benchmarks  Test converting 10,000 good Guids, and 10,000 bad Guids.  Catch FormatException:    10,000 good:     63,668 ticks    10,000 bad:   6,435,609 ticks  Regex Pre-Screen with try-catch:    10,000 good:    637,633 ticks    10,000 bad:     717,894 ticks  COM Interop CLSIDFromString    10,000 good:    126,120 ticks    10,000 bad:      23,134 ticks   p.s. I shouldn't have to justify a question. I'm from the State of Kuwait and hold an Eritrean passport. I'm planning to visit UK in October but my visa will expire in November.    Is it OK to make a journey in the last month of my visa, provided that I make sure that I book my plane back before expiring date? Is it normal for a fast prime to exhibit purple fringing in middle of the image? I have just bought a Nikon 50mm f/1.8D prime lens.  I took this picture (leg of my glasses frame on a mouse, and a LED desk lamp is on top of it) : f1.8, 1/80s, ISO 200   The purple fringing is right in the middle of the picture. Does it happen very often to this lens? ascending/descending in LINQ - can one change the order via parameter? How to start itemize on same line as text? I've created a new environment called 'Example' like this:  \newenvironment{example}     {\textbf{Example:} \begin{itemize}}     {\end{itemize}}   The environment works fine, but the items are starting after the Example: text. Is it possible to start with the first item on the same line as the Example: text and vertically aline the rest of the items with the first item? Lie bracket for Lie algebra of $SO(n,m)$ How does one show that the bracket of elements in the Lie algebra of $SO(n,m)$ is given by  $$[J_{ab},J_{cd}]  ~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$  where $\eta$ has is the definite symmetric form with signature $(n,m)$?