From my personal point of view, we cannot deduce that $NMNM=0$,but I can't find a counterexample.
Let $A$ and $B$ be $n\times n$ matrices such that $ABAB=0_{n\times n}$.  Can we conclude that  $BABA$ must be  $0_{n\times n}$?   I fail to give a counterexample when $n=2$， so I guess the answer is "yes"
Too many of your edits were rejected, try again in 7 days First time I've got the following message on SO:     Too many of your edits were rejected,   try again in 7 days.   Although, I have made ~50 accepted edits this day.  I'm sure that should outweigh the ~5 rejected edits, right?    My suggestion:  bool allowEdit(USER u) {     if(u.rejected * 5 &gt; u.accepted)         return(false);     else         return(true); }   Think of it this way: if I do a 1000 accepted edits, and mess up on 5 [rejected], does that mean I should get banned for 7 days?    Hmmm... There seems to be a bug; the message only appears when clicking edit from review.  But otherwise, I can't edit , even when going to it from the homepage. double perpendicular symbol (for independence) I found from  that I could use the independence symbol:     \newcommand\independent{\protect\mathpalette{\protect\independenT}{\perp}} \def\independenT#1#2{\mathrel{\rlap{$#1#2$}\mkern2mu{#1#2}}}    I was wondering how this works. 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Maybe what I don't understand is: why $(\Sigma \vdash \varphi \implies \Sigma \vdash \forall x \varphi)$ is true but $(\varphi \implies \forall x \varphi)$ is not true?  The book is this: Strange folder in my home folder after a failed run of BleachBit I just would like to know if a question or an answer saved draft is visible to someone else, apart from the OP.  Will a copy of a saved draft remain visible even after it has been deleted? Who has access to it? When the ball is being bounced by the goalkeeper from his hands and a player steals it without touching the goalkeeper (while the goalkeeper is not touching the ball) and scores, is it legal or not?   shows what I'm talking about. Can an inanimate thing lift Mjolnir? Can an inanimate thing can lift Mjolnir without the help of a living being (unworthy)  Scenario 1  Mjolnir in a very light car with a sail attached to it, then a very strong wind blew and moved the car uphill.  It is possible or not?  Scenario 2  Can upward wind alone lift the Mjolnir? Using the same RSA keypair to sign and encrypt The RSA signature operation is basically the same as encrypting with the private key.  In particular, both operations use the same kind of keys.  Is it safe to use the same RSA keypair both for encryption / decryption and for signing / verification? Notify us when the question has been edited after posting an answer Consider this situation. I post a legitimate and correct answer to a question and receive a few upvotes. Then the OP realizes that's not what they wanted to ask, and significantly rewrites the question, rendering my answer irrelevant and useless. Ideally the OP would comment on every answer saying "check my edit" but some people don't know to do that.  This leaves two possibly bad situations:   I never know, the answer stays, and the votes don't reflect the usefulness of the answer anymore. All of a sudden I get an influx of downvotes because my answer isn't helpful anymore. If I'm checking and notice my rep has dropped, I come back after the fact, edit the answer, and bring it back to the original quality. This is great, but 9 times out of 10, the downvoters never come back and notice the answer has been edited. It might get more upvotes, but it still doesn't reflect the true value of the answer.   If we can get notified when the OP gets edited, we can nip it in the bud and go back to edit our answers to match - thus maintaining the quality of the answers on SO. Wine pollutes "Open With" application list The dialog box in question here is the one you get with the context menu option "open with other applications". Wine seems to have inserted more than a dozen or so entries for each application I install, which makes it a pain to find the correct application:     What can I do to remove the duplicates?     Update: Neither of the two solutions really work. The bug is interesting, but the symptoms does not match my problem (I'm not having problem with uninstalling applications, but rather the things that are inserted after installing them), and with the other one, all references to the Wine application are removed, which actually makes the problem worse (although it may be an acceptable solution if nothing else can be found). So this is still an open question; any takers? Schengen Visa Application: what are some helpful tips for preparing? If $A, B$ are two non empty sets of real numbers and for every $a$ from $A$ and $b$ from $B$     $a &lt; b$,   how can I prove that      $\sup A \leq \inf B$? "State-of-the-art" and "technology" I am trying to calculate the sum of this infinite series after having read the series chapter of my textbook: $$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$$  my steps:   $$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}=\sum_{n=1}^{\infty}\frac{2}{4n^2-1}-\sum_{n=1}^{\infty}\frac{1}{4n^2-1}=..help..=sum$$  I am lacking some important properties, I feel I am coming to the right step and cannot spit that out.. Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$ Can someone explain how to prove the following identity involving Fibonacci sequence  $F_n$  $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$ ? What is the physics of a spinning coin? When we spin a coin on a table, we observe 2 things:   It slows down and stops after sometime. It does not stay at just one point on the table but its point of contact with table changes with time.   I was trying to explain quantitatively this but I am stuck at how to take frictional torques into account. Any help will be appreciated. How to filter features in a layer? I am trying to display certain features in a shapefile-based layer using QGIS. I have found the subset function in the properties panel, which does exactly what i want, but is too tedious given that I have to manually sift through a large number of features. Is there a quicker way to do this?  I am using both shapefiles and postGIS best,  dietmar 'had better not entangle' v 'had better not to entangle' Can I write this sentence:     He said Carter had better not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   Like this:     He said Carter had better to not entangle the US in problems like those   in Afghanistan, Somalia and Iraq.   ?  If so, what's the difference between the meaning of both sentence?