Powers of a Matrix

Definition

Let $A$ : Square matrix

Then

$$\begin{array}{rl}{A}^0& =I\\ A^n& =AA\dots A\text{[n factors]}\end{array}$$

If $A$ is invertible

Then

$$A^{-n}=(A^{-1}{)}^n=A^{-1}{A}^{-1}\dots A^{-1}\text{[n factosr]}$$