Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r }
5 & 1 \
- 1 & 2
\end{array} \right] \text { and } B = \left[ \begin{array} { c c }
\frac { 2 } { 11 } & - \frac { 1 } { 11 } \
\frac { 1 } { 11 } & \frac { 5 } { 11 }
\end{array} \right]$$
A) No
B) Yes

Question

Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r } 
5 & 1 \
- 1 & 2
\end{array} \right] \text { and } B = \left[ \begin{array} { c c } 
\frac { 2 } { 11 } & - \frac { 1 } { 11 } \
\frac { 1 } { 11 } & \frac { 5 } { 11 }
\end{array} \right]$$
A) No
B) Yes

Quizplus · Accepted Answer

To determine if matrices A and B are inverses, we can multiply them together. If the product is the identity matrix, then they are inverses. Multiplying A and B gives:$$AB = \left[ \begin{array} { r r } 5 & 1 \-1 & 2\end{array} \right] \left[ \begin{array} { c c } \frac { 2 } { 11 } & - \frac { 1 } { 11 } \\frac { 1 } { 11 } & \frac { 5 } { 11 }\end{array} \right] = \left[ \begin{array} { c c } (5*\frac{2}{11} + 1*\frac{1}{11}) & (5*(-\frac{1}{11}) + 1*\frac{5}{11}) \(-1*\frac{2}{11} + 2*\frac{1}{11}) & (-1*(-\frac{1}{11}) + 2*\frac{5}{11})\end{array} \right]$$$$= \left[ \begin{array} { c c } \frac{10}{11} + \frac{1}{11} & -\frac{5}{11} + \frac{5}{11} \-\frac{2}{11} + \frac{2}{11} & \frac{1}{11} + \frac{10}{11}\end{array} \right] = \left[ \begin{array} { c c } 1 & 0 \0 & 1\end{array} \right]$$Since the product is the identity matrix, A and B are inverses.

Determine Whether a and B Are Inverses A) No B) Yes

Determine Whether a and B Are Inverses A) No
B) Yes