Matrix Calculator - Multiply, Inverse, Determinant & RREF

Matrix AMatrix B

Operation

Result

1922

4350

Enter one matrix row per line. Separate values with spaces or commas. This browser calculator currently supports matrices up to 8 × 8 to keep mobile processing responsive.

How to use the Matrix Calculator

Enter Matrix A using one row per line.
For binary operations such as multiplication, addition or subtraction, enter Matrix B as well.
Choose the matrix operation.
The calculator checks the required matrix dimensions before calculating.
For determinant and inverse operations, Matrix A must be square.
RREF uses row operations to transform the matrix into reduced row echelon form.

Examples

Multiply two 2 × 2 matrices

For A = [[1,2],[3,4]] and B = [[5,6],[7,8]], the product A × B is [[19,22],[43,50]].

Determinant

The determinant of [[1,2],[3,4]] is −2.

Inverse

A square matrix has an inverse only when its determinant is nonzero.

Frequently asked questions

When can two matrices be multiplied?

Matrix A can multiply Matrix B when the number of columns in A equals the number of rows in B.

When does a matrix have an inverse?

A matrix must be square and nonsingular. Equivalently, its determinant must be nonzero.

What is RREF?

Reduced row echelon form is a standardized form produced by elementary row operations. It is useful when solving systems of linear equations and analyzing matrix rank.

Does matrix multiplication commute?

No. In general A × B is not equal to B × A, and one ordering may be defined while the other is not.

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