Determine whether the matrices are inverses.
-$$\left[ \begin{array} { l l }
5 & 3 \
3 & 2
\end{array} \right] , \left[ \begin{array} { r r }
2 & - 3 \
- 3 & 5
\end{array} \right]$$

Question

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { l l } 
5 & 3 \
3 & 2
\end{array} \right] , \left[ \begin{array} { r r } 
2 & - 3 \
- 3 & 5
\end{array} \right]$$

Quizplus · Accepted Answer

To determine if two matrices are inverses, we multiply them. If the product is the identity matrix, then they are inverses. Multiplying the given matrices:$$\left[ \begin{array} { l l } 5 & 3 \3 & 2\end{array} \right]\left[ \begin{array} { r r } 2 & -3 \-3 & 5\end{array} \right]=\left[ \begin{array} { l l } (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.

Determine Whether the Matrices Are Inverses [5332],[2−3−35]\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right][53​32​],[2−3​−35​]

Determine Whether the Matrices Are Inverses $\left[ \begin{array} { l l } 5 & 3 \\3 & 2\end{array} \right] , \left[ \begin{array} { r r } 2 & - 3 \\- 3 & 5\end{array} \right]$