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

Question

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

Quizplus · Accepted Answer

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

Decide Whether or Not the Matrices Are Inverses of Each [5332] and [2−3−35]\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right][53​32​] and [2−3​−35​]

Decide Whether or Not the Matrices Are Inverses of Each $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] \text { and } \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$