Question

Using the matrices below determine if the product of AB is defined. If defined, state the dimension (Picture provided)

Answer 1

option C. Defined, 3 x 3

Explanation:

The order of matrix A is 3 x 2 i.e 3 rows and 2 columns

The order of matrix B is 2 x 3 i.e. 2 rows and 3 columns

Two matrices can be multiplied if and only if the number of columns of 1st matrix is equal to the number of rows of 2nd matrix. Since the number of columns in matrix A is equal to the number of rows in matrix B, the product AB is defined.

The product AB will have number of rows equal to the rows of 1st matrix i.e. matrix A and number of columns equal to the columns of 2nd matrix i.e. matrix B.

So the order of AB will be 3 x 3 .

Therefore, the correct answer is option C. Defined 3 x 3