Definition: Given a square matrix A, and a nonnegative integer n, powers of A are defined as follows:
\(A^2=A A\), \(A^3=A A A\), ...
Few theorems that facilitate calculations of matrix powers:
a) \( A^r A^s = A^{r+s} \);
b) \((A^r)^s = A^{rs} \);
c) if \(A^n\) is invertible, then \( A^{-n}=(A^{-1})^n \) for n>0. Check out our Matrix Inverse Calculator
