Matrix Power Calculator
The matrix power calculator will quickly give you the desired exponent of your 2×2, 3×3, or 4×4 matrix. If you need it, it will even tell you what its diagonalization is (if it exists).
A^52×2result below
Determinant of A^5-1det(A)^k
Trace of the result11
A^5
| 8 | 5 |
| 5 | 3 |
The method
Aᵏ = A × A × … × A, k times
The Fibonacci matrix
The default [[1,1],[1,0]] is worth trying: its kth power holds consecutive Fibonacci numbers, with F(k+1) in the top-left. That gives a way to compute Fibonacci numbers in log(k) steps by repeated squaring rather than k additions.