Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and
the product BA. If either is not defined, say so.
-$$A = \left[ \begin{array} { l l }
3 & 4
\end{array} \right] ; B = \left[ \begin{array} { r }
- 3 \
6
\end{array} \right]$$
A) $\mathrm { AB }$ is not defined; $\mathrm { BA }$ is $2 \times 2$.
B) $\mathrm { AB }$ is $1 \times 1$; BA is $2 \times 2$.
C) $\mathrm { AB }$ is $1 \times 1$; $\mathrm { BA }$ is not defined.
D) $\mathrm { AB }$ is $2 \times 2$; $\mathrm { BA }$ is $1 \times 1$.

Question

Either the dimensions of two matrices or the matrices themselves are given. Find the dimensions of the product AB and
the product BA. If either is not defined, say so.
-$$A = \left[ \begin{array} { l l } 
3 & 4
\end{array} \right] ; B = \left[ \begin{array} { r } 
- 3 \
6
\end{array} \right]$$
A) $\mathrm { AB }$ is not defined; $\mathrm { BA }$ is $2 \times 2$.
B) $\mathrm { AB }$ is $1 \times 1$; BA is $2 \times 2$.
C) $\mathrm { AB }$ is $1 \times 1$; $\mathrm { BA }$ is not defined.
D) $\mathrm { AB }$ is $2 \times 2$; $\mathrm { BA }$ is $1 \times 1$.

Quizplus · Accepted Answer

Matrix A is 1x2 and matrix B is 2x1. The product AB is defined and results in a 1x1 matrix. The product BA is defined and results in a 2x2 matrix.

Either the Dimensions of Two Matrices or the Matrices Themselves A=[34];B=[−36]A = \left[ \begin{array} { l l } 3 & 4\end{array} \right] ; B = \left[ \begin{array} { r } - 3 \\6\end{array} \right]A=[3​4​];B=[−36​]

Either the Dimensions of Two Matrices or the Matrices Themselves $A = \left[ \begin{array} { l l } 3 & 4\end{array} \right] ; B = \left[ \begin{array} { r } - 3 \\6\end{array} \right]$