Question

Paul found the inverse of ... to be ... Which calculations will confirm that his (or her) answer is correct? Select all that apply.

Answer 1

Let A be an invertible matrix; therefore, if B is its inverse, according to the inverse matrix definition,

$AB=BA=I_{n\times n}$

Therefore, in our case,

$A=\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix},B=\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix},I_{n\times n}=I_{2\times2}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}$

Then,

$\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix}\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix}=\begin{bmatrix}{-3} & {8} \\ {2} & {-5}\end{bmatrix}\begin{bmatrix}{5} & {8} \\ {2} & {3}\end{bmatrix}=\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}$

Hence, the answers are options B and C