The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, whenever these
products exist.
-A is $ 2 \times 1 $, and $ B $ is $ 1 \times 1 $.
A) $ \mathrm{AB} $ does not exist; $ 1 \times 2 $
B) $ 2 \times 2 ; 1 \times 1 $
C) $ 1 \times 2 ; 1 \times 1 $
D) $ 2 \times 1 $; BA does not exist.

Question

Quizplus · Accepted Answer

For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix. Since A is $2 \times 1$ and B is $1 \times 1$, AB exists and will be $2 \times 1$. However, for BA, the number of columns in B (1) does not match the number of rows in A (2), so BA does not exist.

The Sizes of Two Matrices a and B Are Given 2×1 2 \times 1 2×1

The Sizes of Two Matrices a and B Are Given $2 \times 1$