The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product
can be calculated.
-$A$ is $1 \times 3 ; B$ is $3 \times 1$.
A) $\mathrm { AB }$ cannot be calculated; $\mathrm { BA }$ is $3 \times 3$.
B) $\mathrm { AB }$ is $3 \times 3$; $\mathrm { BA }$ is $1 \times 1$.
C) $\mathrm { AB }$ is $1 \times 1$; BA cannot be calculated.
D) $\mathrm { AB }$ is $1 \times 1$; $\mathrm { BA }$ is $3 \times 3$.

Question

Quizplus · Accepted Answer

The product $AB$ can be calculated because the number of columns in $A$ matches the number of rows in $B$, resulting in a $1 \times 1$ matrix. The product $BA$ can also be calculated because the number of columns in $B$ matches the number of rows in $A$, resulting in a $3 \times 3$ matrix.

The Sizes of Two Matrices Are Given AAA Is 1×3;B1 \times 3 ; B1×3;B

The Sizes of Two Matrices Are Given $A$ Is $1 \times 3 ; B$