Question

Find x such that the matrix is equal to its own inverse. A = left[3 x , -2 -3right]

Matrices
Find x such that the matrix is equal to its own inverse.
$$A = \left[3 x , -2 -3\right]$$

2021-02-26
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: $$x = 4$$