Cool simple solution to: $-A^2$ is not the identity matrix this is not a question per se, just a simple cool solution to a potentially difficult question, that I want to share. I liked it.  The question is:  Let $A$ be a $3\times3$ matrix with real values. Show that $A^2 \neq -I_3$  There are probably many solutions for this problem, but i really thought this one was simple.  Solution is posted down below.
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$? Is it possible for a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$,  $$\mathbf{A}^2=-\mathbf{I}$$  I know that It is possible for $2\times2$ matrix, but is it possible for $3\times3$ matrix ?
Ubuntu 19.04 problems install upgrades How would I be able to create a grill of sorts found on the front of some computer cases such as this one Are proofs by contradiction really logical? How do you use the Dungeon Defender's Portal Gun? The topic pretty much sums up my question. I have not yet figured out how the gun operates aside from the fact that it creates Portal portals. The weapon description indicates that it deals 250+ base damage, but how is that damage applied to the monsters? What's a good word for a person, or a state, when a person is constantly waiting for life to get good, but does nothing to actually make it happen I've written a song about people who constantly wait for something good to happen to them and am looking for a word to describe this state/paradox/condition.   The song is about people who expect life to get better for no reason, talk about moving to a bigger city or a different place as if that would magically make them rich, famous and happy, and keep talking about how they are going to do this or that, but never do it. I was under the impression that there's a psychological term for this state, but can't google it up, so I probably made it up.  This is essentially a song about myself, I keep talking about how I love to make music, or shoot videos, but I never actually produce anything, yet it's the only thing I can think of. When it comes to the moment to take action – I just stay at home watching tv shows.  I know it's a broad question and list of topics, but I guess I'm looking for a word that describes this state – of doing NOTHING. My stance is that these websites are a great boon to the research community and they were certainly extremely helpful for my research. I think they should be applauded rather than persecuted, and while they may be illegal now, I think a way to make them legal should be found (in the same way I can download articles legally through my university's subscription to all the major publishers and journals).  Can I thank them in the acknowledgements section of my thesis? Trying to find a story about an unborn telepathic baby who can save a spaceship from doom I am running Ubuntu Gnome 16.10 (64bit). Gnome-shell version 3.20.4.   When I start my computer, I eventually see GDM3 offering a login prompt, as expected.   After I login, my monitors flash a little (like they're unplugged and then replugged in), and then I am brought to the gnome 3 desktop.   However, if I hit  CTRL + ALT + F1, I am brought back to GDM3, offering a login prompt.   If I then hit CTRL + ALT + F2,  I am brought back to my Gnome 3 desktop.  So it seems like GDM3 continues to run in TTY1 while the desktop runs in TTY2.   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Considering the following MWE file:  \documentclass[tikz]{standalone}  \usepackage{tikz} \usepackage{pgfplots} \pgfplotsset{compat=newest} \usepackage{amsmath}  \begin{document}      \begin{tikzpicture}         \begin{axis}[%             width=16cm,height=8cm,             view={-45}{65},             scale only axis,             xmin=200,xmax=500,             xlabel={data1},             ymin=0,ymax=100,             ylabel={data2},             zmin=0,zmax=1,             zlabel={data3},         ]         \addplot3 [             thick,smooth,             color= darkgray,             solid]             table[row sep=crcr] {                 250 0 0\\                 250 25 0.2\\                 250 50 0.3\\                 250 75 0.2\\                 250 100 0\\             };          \addplot3 [             thick,smooth,             color= darkgray,             solid]             table[row sep=crcr] {                 450 0 0.5\\                 450 25 0.1\\                 450 50 0\\                 450 75 0.1\\                 450 100 0.5\\             };         \end{axis}     \end{tikzpicture}% \end{document}   How can I plot only the first n=4 rows of each table and ask pgfplots to stop reading the table once this row is reached ?  Of course, for the above example, this seems useless, but when huge data tables are used, this could be extremely usefull, in particular to use the same data and focus on different parts of the table in different figures. Our son is about to turn 3 months but he is yet to sleep on his own (as in we put him to sleep, put him down on the crib then he sleeps for few hours). He only sleeps when he is carried during the day, the moment we put him down he wakes up crying. At night, he sleeps with us on the bed where he is right next to his mommy. We blame ourselves for letting this happen but now my wife can't do anything during the day but carry him.  What can we do to break him out of this habit? Any pointers would be great appreciated. In C, how do I restrict the scope of a global variable to the file in which it's declared? Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$ How do you create product mock-ups? 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The linking verbs include the following: the helping verbs is: am, are, was, were, be, being, and been; the sense verbs: look, taste, smell, feel, and sound; and verbs like become, seem, appear, grow, continue, stay, and turn.   Or is it a past participle because the clause is in the passive voice?   Does “he is buried” mean currently his body lies in a coffin covered with soil, or  does it mean he has been buried by someone?  If we say ‘he was buried’ it clearly refers to an event that happened and ended sometime in the past. It might even suggest that the burial ground has since been changed.