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

Paul Found The Inverse Of To Be Which Calculations Will Confirm That His Or Her Answer Is Correct Select All That Apply class=

Sagot :

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

[tex]AB=BA=I_{n\times n}[/tex]

Therefore, in our case,

[tex]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}[/tex]

Then,

[tex]\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}[/tex]

Hence, the answers are options B and C

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