I am having problem with how to calculate a matrices that are raised to negative powers. I can manage the adding, multiplication etc, but I am stuck here.
The matrix in question is $A=\begin{bmatrix}5&-2\\10&-4\end{bmatrix}$. It is a $2\times 2$ matrix. I need to find what this matrix is raised to the power $-1$.
I preferably don't just want an answer, but a summary of how to do these as I have numerous others that I need to do. Any help will be much appreciated!
Best Answer
You should know that if $A$ is a square matrix, then $A^{-1}$ denotes its inverse matrix if it exists. For the particular matrix you mentioned, the inverse does not exist. Can you see why?