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by **king&i** on Wed Sep 09, 2009 7:22 pm

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

**Sponsor**

by **stapel_eliz** on Wed Sep 09, 2009 9:20 pm

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

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

See where this leads.... :wink:

by **nona.m.nona** on Thu Sep 17, 2009 6:42 pm

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.

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

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

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