Question

Let A and B be arbitrary matrices for which the indicated product is defined. Determine whether the statement below is true or false, and justify the answer. If A is a 3x3 matrix and B is a 3x3 matrix, then AB is defined.

Answer 1

The statement is true. If A is a 3x3 matrix and B is a 3x3 matrix, then the product AB is defined.

Step-by-step explanation:

The statement is true. If A is a 3x3 matrix and B is a 3x3 matrix, then the product AB is defined.

In order for the product AB to be defined, the number of columns in matrix A must be equal to the number of rows in matrix B. Since both A and B are 3x3 matrices, this condition is satisfied.

The resulting product matrix AB will also be a 3x3 matrix, where each element in the product matrix is computed by taking the dot product of the corresponding row in matrix A and the corresponding column in matrix B.