## is there a 2x2 matrix A so A2 = -I?

Linear spaces and subspaces, linear transformations, bases, etc.
king&i
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Joined: Sat Mar 07, 2009 5:13 pm

### is there a 2x2 matrix A so A2 = -I?

is there a 2x2 matrix A so A2 = -I?
(I is ident matrix)

stapel_eliz
Posts: 1734
Joined: Mon Dec 08, 2008 4:22 pm
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Hint: Try a 2-by-2 matrix $A$ with zeroes on the diagonal:

. . . . .$A\, =\, \left[\begin{array}{cc}0&a\\b&0\end{array}\right]$

nona.m.nona
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### Re: is there a 2x2 matrix A so A2 = -I?

In case you're still working on this:

$A\, =\, \left[\begin{array}{cc}0&a\\b&0\end{array}\right]$
$A^2\, =\, \left[\begin{array}{cc}0&a\\b&0\end{array}\right]\left[\begin{array}{cc}0&a\\b&0\end{array}\right]\, =\, \left[\begin{array}{cc}0+ab&0\\0&ab+0\end{array}\right]\, =\, \left[\begin{array}{cc}-1&0\\0&-1\end{array}\right]$

Now solve. There is more than one solution.