Question

Define the product of two matrices A and B. When is this product defined?

Short answer

Product of matrix: Number of columns in the first matrix = Number of rows in the second matrix.

Step-by-step solution

Step: 1 Introduction of matrix and binary operation

Matrix multiplication is a binary operation that produces a matrix from two matrices. The resulting matrix, known as the matrix product, has the number of columns of the first and number of rows the second matrix. The product of matrices A and B is denoted by AB.

Step: 2 Matrix multiplication

Finding the product of two matrices is only possible when the inner dimension is the same; meaning that the number of columns of the first matrix is equal to the number of columns of the first matrix is equal to the number of rows of the second matrix.