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Linear Algebra

Matrix Multiplication

Matrix multiplication combines two matrices so that each entry of the product is the dot product of a row of A with a column of B. The number of columns of A must equal the number of rows of B.

Matrix Multiplication

Multiply two matrices A·B.

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Frequently asked questions

When can two matrices be multiplied?

Only when the number of columns of the first matrix equals the number of rows of the second.

Is matrix multiplication commutative?

No. In general A·B is not equal to B·A, and one product may not even be defined.

What are the dimensions of the product?

If A is m×n and B is n×p, the product A·B is an m×p matrix.

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