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Matrix Power Calculator

Compute Aⁿ for any integer exponent n — positive, negative or zero. Small exponents multiply out step by step, large ones use fast squaring, and negative powers build on the exact inverse.

Computed

The power and the full working are shown below.

Input matrix Afractions allowed

Integers, negatives, decimals or fractions (e.g. 3, -2, 1/2). Empty cells count as 0.

Result Aⁿexact

Step-by-step solution

1
Start: the matrix A
We want A². The matrix is square, so integer powers are well defined.
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A² = A¹ · A¹
Multiply the matrix by itself: each entry of the product is the dot product of a row with a column.
$A^{2} = A^{1} \cdot A^{1}$
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Result: A²
Repeated multiplication — 1 matrix multiplication in total.
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Determinant check
det(A) = 0, so det(A²) = (det A)^2 = 0 — matching the determinant of the result.
$\det\left(A^{2}\right) = \left(\det A\right)^{2} = 0$

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Matrix Power Calculator

Step-by-step solution

Start: the matrix A

A² = A¹ · A¹

Result: A²

Determinant check