Using matrix $A=\left[\begin{array}{rrr}
3 & 7 & 4 \
2 & -1 & 6
\end{array}\right]$ and $B=\left[\begin{array}{rrr}
-1 & 5 & 2 \
7 & 10 & 1 \
-2 & 5 & -1
\end{array}\right]$ which of the following is a true statement?
A) Matrix A has an inverse.
B) $A+B=\left[\begin{array}{rrr}
2 & 12 & 6 \
9 & 9 & 7 \
-2 & 5 & -1
\end{array}\right]$
C) AB exists and BA does not exist.
D) BA exists and AB does not exist.

Question

Using matrix $A=\left[\begin{array}{rrr}
3 & 7 & 4 \
2 & -1 & 6
\end{array}\right]$ and $B=\left[\begin{array}{rrr}
-1 & 5 & 2 \
7 & 10 & 1 \
-2 & 5 & -1
\end{array}\right]$ which of the following is a true statement?
A) Matrix  A  has an inverse.
B) $A+B=\left[\begin{array}{rrr}
2 & 12 & 6 \
9 & 9 & 7 \
-2 & 5 & -1
\end{array}\right]$
C)  AB  exists and  BA  does not exist.
D)  BA  exists and  AB  does not exist.

Quizplus · Accepted Answer

DMatrix multiplication is defined if the number of columns in the first matrix is equal to the number of rows in the second matrix. Since $A$ is a $2 \times 3$ matrix and $B$ is a $3 \times 3$ matrix, $AB$ exists because the number of columns in $A$ (3) matches the number of rows in $B$ (3). However, $BA$ does not exist because the number of columns in $B$ (3) does not match the number of rows in $A$ (2).

Using Matrix A=[3742−16]A=\left[\begin{array}{rrr}3 & 7 & 4 \\2 & -1 & 6\end{array}\right]A=[32​7−1​46​]

Using Matrix $A=\left[\begin{array}{rrr}3 & 7 & 4 \\2 & -1 & 6\end{array}\right]$