Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { r r }
6 & - 5 \
- 3 & 5
\end{array} \right] \text { and } \left[ \begin{array} { c c }
\frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 5 } & \frac { 2 } { 5 }
\end{array} \right]$$
A) Yes
B) No

Question

Decide whether or not the matrices are inverses of each other.
-$$\left[ \begin{array} { r r } 
6 & - 5 \
- 3 & 5
\end{array} \right] \text { and } \left[ \begin{array} { c c } 
\frac { 1 } { 3 } & \frac { 1 } { 3 } \
\frac { 1 } { 5 } & \frac { 2 } { 5 }
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

To determine if two matrices are inverses of each other, we can multiply them and see if the result is the identity matrix. Multiplying the given matrices:$$\left[ \begin{array} { r r } 6 & -5 \-3 & 5\end{array} \right]\left[ \begin{array} { c c } \frac { 1 } { 3 } & \frac { 1 } { 3 } \\frac { 1 } { 5 } & \frac { 2 } { 5 }\end{array} \right]=\left[ \begin{array} { c c } (6)\left(\frac{1}{3}\right) + (-5)\left(\frac{1}{5}\right) & (6)\left(\frac{1}{3}\right) + (-5)\left(\frac{2}{5}\right) \(-3)\left(\frac{1}{3}\right) + (5)\left(\frac{1}{5}\right) & (-3)\left(\frac{1}{3}\right) + (5)\left(\frac{2}{5}\right)\end{array} \right]=\left[ \begin{array} { c c } 2 - 1 & 2 - 2 \-1 + 1 & -1 + 2\end{array} \right]=\left[ \begin{array} { c c } 1 & 0 \0 & 1\end{array} \right]$$The result is the identity matrix, indicating that the two matrices are indeed inverses of each other.

Decide Whether or Not the Matrices Are Inverses of Each