Matrix Power Calculator
Compute Aⁿ for a square matrix A and any integer exponent n, including the identity for n = 0 and inverse-based negative powers.
- 1
Product a·d
2 × 3 = 6 - 2
Product b·c
0 × 1 = 0 - 3
Determinant det(A)
6 − 0 = 6Determinant of the base matrix A — non-zero means negative powers exist.
How does this calculator work?
A matrix power raises a square matrix A to an integer n. For n = 0 the result is the identity matrix, for n > 0 you multiply A by itself n times, and for n < 0 you invert A (requires a non-zero determinant) and raise the inverse to |n|. Enter rows of numbers and an exponent to get Aⁿ.
Formula
How this is calculated
Enter a square matrix A with one row per line, separating entries by spaces or commas, and an integer exponent n. The matrix must have the same number of rows and columns; otherwise the power is undefined.
For n = 0 the result is the n×n identity matrix Iₙ. For n > 0 the matrix is multiplied by itself repeatedly (Cₖ₊₁ = Cₖ · A), using standard row-by-column matrix multiplication. For n < 0 the calculator first computes the inverse A⁻¹ via the adjugate (transpose of the cofactor matrix) divided by det(A), then raises that inverse to |n|. Negative powers therefore require det(A) ≠ 0.
Entries can be integers or decimals. The determinant is computed by cofactor (Laplace) expansion, which is exact for the small matrices typical of hand calculations but can accumulate floating-point rounding for larger sizes. Results are shown to four decimal places.
Frequently asked questions
By convention A⁰ equals the identity matrix Iₙ of the same size, just as x⁰ = 1 for numbers.
Yes. A⁻ⁿ is computed as (A⁻¹)ⁿ, which exists only when the matrix is invertible, i.e. its determinant is non-zero.
Matrix multiplication A · A is only defined when the number of columns equals the number of rows, which forces A to be square for any power.
Also known as
TG we-Calculate Editorial Team. (2026). Matrix Power Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/matrix-power-calculator
TG we-Calculate Editorial Team. "Matrix Power Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/matrix-power-calculator.
TG we-Calculate Editorial Team, "Matrix Power Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/matrix-power-calculator
@misc{wecalculate_matrix_power_calculator, title = {Matrix Power Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/matrix-power-calculator}}, year = {2026}, note = {TG we-Calculate} }
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