Any square matrix raised to the power 0 is the identity matrix — ones on the diagonal and zeros elsewhere.

A^1 equals the original matrix A unchanged.

Is the exponent limited?

The tool accepts non-negative integer exponents from 0 to 20. Higher powers can produce very large numbers; use scientific notation if values overflow.

Does this support rectangular matrices?

No. Matrix exponentiation is only defined for square matrices. This tool supports 2x2 and 3x3 square matrices.

Are decimal entries allowed?

Yes. You may enter decimals such as 0.5 or -1.25. Results are rounded to 6 significant figures to avoid floating-point noise.

Each intermediate result A^k (for k from 2 up to n) is displayed as a collapsible step, so you can trace every multiplication.

Matrix Power Calculator

Name: Matrix Power Calculator
Availability: InStock
Author: Nham Vu

Enter a 2x2 or 3x3 matrix and an integer exponent to compute A^n with full step-by-step multiplication.

Matrix Input

Matrix Size

Matrix A

Exponent n (0 – 20)

Quick Examples

Fill in the matrix and click Calculate A^n

Summary

Enter a 2x2 or 3x3 matrix and an integer exponent to compute A^n with full step-by-step multiplication.

How it works

Choose a matrix size: 2x2 or 3x3.
Fill in the matrix cells with integer or decimal values.
Enter an integer exponent n (0 through 20).
Click Calculate — the tool performs repeated matrix multiplication A × A × … × A.
The result matrix and each intermediate step are displayed below.

Use cases

Verify matrix exponentiation homework answers.
Compute Markov chain transition probabilities over n steps.
Check results when studying linear algebra or graph theory.
Understand how diagonal and non-diagonal matrices behave under repeated multiplication.
Quickly raise a transformation matrix to a power for computer graphics work.
Test numerical stability of matrix operations.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu

Matrix Power Calculator

Matrix Input

Result: A^2