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 $2 \times 1$; B is $1 \times 1$.
A) $\mathrm { AB }$ cannot be calculated; $\mathrm { BA }$ is $1 \times 2$.
B) $\mathrm { AB }$ is $1 \times 2$; $\mathrm { BA }$ is $1 \times 1$.
C) $\mathrm { AB }$ is $2 \times 1$; BA cannot be calculated.
D) $\mathrm { AB }$ is $2 \times 2$; $\mathrm { BA }$ is $1 \times 1$.

Question

Quizplus · Accepted Answer

Matrix multiplication is possible if the number of columns in the first matrix is equal to the number of rows in the second matrix. For AB, A is $2 \times 1$ and B is $1 \times 1$, so AB can be calculated and will be $2 \times 1$. For BA, B is $1 \times 1$ and A is $2 \times 1$, so BA cannot be calculated due to the mismatch in dimensions.

The Sizes of Two Matrices Are Given 2×12 \times 12×1 ; B Is

The Sizes of Two Matrices Are Given $2 \times 1$ ; B Is