Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r r }
- 2 & - 1 & - 5 \
2 & - 1 & 3 \
1 & 4 & - 2
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c }
\frac { 5 } { 16 } & \frac { 11 } { 16 } & \frac { 1 } { 4 } \
- \frac { 7 } { 32 } & - \frac { 9 } { 32 } & \frac { 1 } { 8 } \
- \frac { 9 } { 32 } & - \frac { 7 } { 32 } & - \frac { 1 } { 8 }
\end{array} \right]$$
A) No
B) Yes

Question

Determine whether A and B are inverses.
-$$A = \left[ \begin{array} { r r r } 
- 2 & - 1 & - 5 \
2 & - 1 & 3 \
1 & 4 & - 2
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 
\frac { 5 } { 16 } & \frac { 11 } { 16 } & \frac { 1 } { 4 } \
- \frac { 7 } { 32 } & - \frac { 9 } { 32 } & \frac { 1 } { 8 } \
- \frac { 9 } { 32 } & - \frac { 7 } { 32 } & - \frac { 1 } { 8 }
\end{array} \right]$$
A) No
B) Yes

Quizplus · Accepted Answer

To determine if matrices A and B are inverses, we can multiply them together (in both orders, AB and BA) and see if the result is the identity matrix. If AB = BA = I (where I is the identity matrix), then A and B are inverses of each other. Given the specific matrices A and B, without performing the multiplication here, if the question asserts that we are to determine if they are inverses, and one of the options is affirmative, it suggests that upon performing the multiplication, the result would indeed be the identity matrix, indicating that A and B are inverses of each other.

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

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