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

Question

Quizplus · Accepted Answer

To determine if two matrices are inverses of each other, we can multiply them and see if the product is the identity matrix. Multiplying the given matrices:$\left[ \begin{array} { l l } 5 & 3 \ 3 & 2 \end{array} \right] \times \left[ \begin{array} { r r } 2 & - 3 \ - 3 & 5 \end{array} \right] = \left[ \begin{array} { c c } 10 - 9 & -15 + 15 \ 6 - 6 & -9 + 10 \end{array} \right] = \left[ \begin{array} { c c } 1 & 0 \ 0 & 1 \end{array} \right]$Since the product is the identity matrix, the matrices are inverses of each other.

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

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