Matrix Powers Calculator

2x2
3x3
4x4
5x5
6x6
7x7
8x8

Basic Information

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