Determine which pair of matrices is an inverse pair.
A) $\left[ \begin{array} { l l }
0 & 3 \
3 & 0
\end{array} \right] \left[ \begin{array} { c c }
0 & \frac { 1 } { 3 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$
B) $\left[ \begin{array} { l l }
3 & 3 \
0 & 3
\end{array} \right] \left[ \begin{array} { c c }
0 & - 3 \
- 3 & 3
\end{array} \right]$
C) $\left[ \begin{array} { l l }
0 & 3 \
3 & 0
\end{array} \right] \left[ \begin{array} { l l }
0 & 3 \
3 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l }
3 & 0 \
0 & 3
\end{array} \right] \left[ \begin{array} { c c }
0 & \frac { 1 } { 3 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$
E) None of these

Question

Determine which pair of matrices is an inverse pair.  
A) $\left[ \begin{array} { l l } 
0 & 3 \
3 & 0
\end{array} \right] \left[ \begin{array} { c c } 
0 & \frac { 1 } { 3 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$
B) $\left[ \begin{array} { l l } 
3 & 3 \
0 & 3
\end{array} \right] \left[ \begin{array} { c c } 
0 & - 3 \
- 3 & 3
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
0 & 3 \
3 & 0
\end{array} \right] \left[ \begin{array} { l l } 
0 & 3 \
3 & 0
\end{array} \right]$
D) $\left[ \begin{array} { l l } 
3 & 0 \
0 & 3
\end{array} \right] \left[ \begin{array} { c c } 
0 & \frac { 1 } { 3 } \
\frac { 1 } { 3 } & 0
\end{array} \right]$
E) None of these

Quizplus · Accepted Answer

Two matrices are inverses of each other if their product is the identity matrix. In option A, multiplying the two matrices results in the identity matrix, indicating they are inverse pairs.

Determine Which Pair of Matrices Is an Inverse Pair B) [3303][0−3−33]\left[ \begin{array} { l l } 3 & 3 \\0 & 3\end{array} \right] \left[ \begin{array} { c c } 0 & - 3 \\- 3 & 3\end{array} \right][30​33​][0−3​−33​]

Determine Which Pair of Matrices Is an Inverse Pair B) $\left[ \begin{array} { l l } 3 & 3 \\0 & 3\end{array} \right] \left[ \begin{array} { c c } 0 & - 3 \\- 3 & 3\end{array} \right]$