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What are the dimensions of the matrix product?

Ask by Flynn Coleman. in the United States
Jan 20,2025

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The matrix product \( AB \) has dimensions \( m \times p \), where \( A \) is \( m \times n \) and \( B \) is \( n \times p \).

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Mind Expander

When you multiply two matrices, the resulting product matrix’s dimensions depend on the dimensions of the matrices being multiplied. If you have a matrix A of size m x n and a matrix B of size n x p, the product matrix AB will have dimensions m x p. Just remember: the number of columns in the first matrix (A) must equal the number of rows in the second matrix (B) for multiplication to be possible! So, if you're ever in doubt, just check those dimensions before you dive into matrix multiplication! Keeping track of those rows and columns can save you from some hefty calculation woes and mistakes.

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