When you multiply this matrix by itself, the first element is 9-2x that has to be equal to 1.

\(9-2x=1\)

\(-2x=-8\)

\(x=4\)

So the answer \(x = 4\) then the matrix is its own inverse!

\(\left[\left[3,x\right],\left[-2,-3\right]^2=\left[\left[9-2x,3x-3x\right],\left[-6+6\right],\left[-2x+9\right]\right]\right]\)

when \(x = 4\) then

\(\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)

Result: \(x = 4\)

\(9-2x=1\)

\(-2x=-8\)

\(x=4\)

So the answer \(x = 4\) then the matrix is its own inverse!

\(\left[\left[3,x\right],\left[-2,-3\right]^2=\left[\left[9-2x,3x-3x\right],\left[-6+6\right],\left[-2x+9\right]\right]\right]\)

when \(x = 4\) then

\(\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)

Result: \(x = 4\)