Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { l l }
- 5 & 1 \
- 7 & 1
\end{array} \right] \text { and } \left[ \begin{array} { l l }
\frac { 1 } { 2 } & - \frac { 1 } { 2 } \
\frac { 7 } { 2 } & - \frac { 5 } { 2 }
\end{array} \right]$$
A) Yes
B) No

Question

Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { l l } 
- 5 & 1 \
- 7 & 1
\end{array} \right] \text { and } \left[ \begin{array} { l l } 
\frac { 1 } { 2 } & - \frac { 1 } { 2 } \
\frac { 7 } { 2 } & - \frac { 5 } { 2 }
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

To determine if two matrices are inverses of each other, we multiply them. If the product is the identity matrix, then they are inverses. Multiplying the given matrices:$$\left[ \begin{array} { l l } - 5 & 1 \- 7 & 1\end{array} \right]\left[ \begin{array} { l l } \frac { 1 } { 2 } & - \frac { 1 } { 2 } \\frac { 7 } { 2 } & - \frac { 5 } { 2 }\end{array} \right]=\left[ \begin{array} { l l } - \frac { 5 } { 2 } + \frac { 7 } { 2 } & \frac { 5 } { 2 } - \frac { 5 } { 2 } \- \frac { 7 } { 2 } + \frac { 7 } { 2 } & \frac { 7 } { 2 } - \frac { 5 } { 2 }\end{array} \right]=\left[ \begin{array} { l l } 1 & 0 \0 & 1\end{array} \right]$$The product is the identity matrix, so the matrices are inverses of each other.

Decide Whether or Not the Matrices Are Inverses of Each