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

Question

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

Quizplus · Accepted Answer

To determine if matrices A and B are inverses, we need to check if their product (in both orders, AB and BA) is the identity matrix. The identity matrix in this case is a 2x2 matrix with ones on the diagonal and zeros elsewhere. First, calculate AB:$$AB = \left[ \begin{array}{cc} 4 & 1 \ 2 & 2 \end{array} \right] \left[ \begin{array}{rr} 3 & -2 \ -11 & 8 \end{array} \right] = \left[ \begin{array}{cc} 12-11 & -8+8 \ 6-22 & -4+16 \end{array} \right] = \left[ \begin{array}{cc} 1 & 0 \ -16 & 12 \end{array} \right]$$This result is not the identity matrix, so we can conclude that A and B are not inverses without needing to calculate BA.

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

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