[Math] negative power on a matrix

Question

I have a compute a calculus with a negative power on a matrix, however, due of my low math level, I am not sure on how powers and moreover negative ones applies on matrices could you give me some advices ? this calculus is this one:

Answer 1

Given a square matrix $A$, $A^{-1}$ is the inverse of A, that exists iff $\det A \ne0$.

For $2\times2$ matrix it is: $$ \begin{bmatrix} a&b\\c&d \end{bmatrix}^{-1}= \begin{bmatrix} d&-b\\-c&a \end{bmatrix}\frac{1}{\det A} $$