Decide whether or not matrix A and matrix B are inverses.
-$$\mathrm { A } = \left[ \begin{array} { r r }
- 2 & 4 \
4 & - 4
\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l }
1 / 2 & 1 / 4 \
1 / 2 & 1 / 4
\end{array} \right]$$
A) Yes
B) No

Question

Decide whether or not matrix A and matrix B are inverses.
-$$\mathrm { A } = \left[ \begin{array} { r r } 
- 2 & 4 \
4 & - 4
\end{array} \right] \text { and } \mathrm { B } = \left[ \begin{array} { l l } 
1 / 2 & 1 / 4 \
1 / 2 & 1 / 4
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

To determine if matrices A and B are inverses, we can multiply them and see if the result is the identity matrix. Multiplying A and B gives:$$\left[ \begin{array} { r r } - 2 & 4 \4 & - 4\end{array} \right]\left[ \begin{array} { l l } 1 / 2 & 1 / 4 \1 / 2 & 1 / 4\end{array} \right]=\left[ \begin{array} { c c }0 & 0 \0 & 0\end{array} \right]$$This result is not the identity matrix, which would have 1s on the diagonal and 0s elsewhere. Therefore, A and B are not inverses.

Decide Whether or Not Matrix a and Matrix B Are