The size of two matrices is given. Find the size of the product AB and the product BA, if the products exist.
-A is 2 × 1, B is 1 × 1.
A) AB is 2 × 1, BA is undefined.
B) AB is 2 × 2, BA is 1 × 1.
C) AB is undefined, BA is 1 × 2.
D) AB is 1 × 2, BA is 1 × 1.

Question

Quizplus · Accepted Answer

Matrix multiplication is defined when the number of columns in the first matrix is equal to the number of rows in the second matrix. For AB, A is 2 × 1 and B is 1 × 1, so AB is defined and results in a 2 × 1 matrix. For BA, B is 1 × 1 and A is 2 × 1, so BA is undefined because the number of columns in B does not match the number of rows in A.

The Size of Two Matrices Is Given