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

Linear spaces and subspaces, linear transformations, bases, etc.

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

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

Posts: 24
Joined: Sat Mar 07, 2009 5:13 pm

Hint: Try a 2-by-2 matrix $A$ with zeroes on the diagonal:

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

stapel_eliz

Posts: 1705
Joined: Mon Dec 08, 2008 4:22 pm

### 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.
nona.m.nona

Posts: 248
Joined: Sun Dec 14, 2008 11:07 pm