I've A^-1 = - A What is A

I've figured that A^2= -I but what's then?

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- Jan 14th 2012, 12:43 PMahmedzoro10Matrix inversion problem
I've A^-1 = - A What is A

I've figured that A^2= -I but what's then? - Jan 14th 2012, 12:55 PMalexmahoneRe: Matrix inversion problem
- Jan 14th 2012, 01:05 PMOpalgRe: Matrix inversion problem
- Jan 14th 2012, 01:12 PMahmedzoro10Re: Matrix inversion problem
How did you get this one?

- Jan 14th 2012, 01:29 PMalexmahoneRe: Matrix inversion problem
- Jan 14th 2012, 01:32 PMalexmahoneRe: Matrix inversion problem
- Jan 15th 2012, 11:27 AMHallsofIvyRe: Matrix inversion problem
Let $\displaystyle A= \begin{bmatrix}a & b \\ c & d\end{bmatrix}$. Then $\displaystyle A^2= \begin{bmatrix}a^2+ bd & ab+ bd \\ ac+ cd & bc+ d^2\end{bmatrix}= \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. So we must have $\displaystyle a^2+ bd= 1$, $\displaystyle ab+ bd= 0$, $\displaystyle ac+ cd= 0$, and $\displaystyle bc+ d^2= 1$. You might try things like taking b (or c) equal to 0 or not equal to 0 and see what you get.