Matrix Powers Calculator

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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
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