$\begin{bmatrix} x&-x \\ -x&x \end{bmatrix}$*$\begin{bmatrix} a&b \\ c&d \end{bmatrix}$ = $\begin{bmatrix} x&-x \\ -x&x \end{bmatrix}$
on solving we get, a - c = 1 and d – b = 1 so, any value of a,b in following matrix can be Identity matrix.
$\begin{bmatrix} a+1&b \\ a&b+1 \end{bmatrix}$