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If P = \(\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatri...

If P = $\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}$ , what is P $^-1$

A.

$\begin{pmatrix} -{\frac{1}{5}} & -{\frac{3}{5}} \\ -{\frac{1}{5}} & -{\frac{2}{5}} \end{pmatrix}$

B.

$\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ {\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}$

C.

$\begin{pmatrix} -{\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}$

D.

$\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}$

View answer & explanation

Correct answer is D

P = $\begin{pmatrix} 2 & -3 \\ 1 & 1 \end{pmatrix}$

|P| = 2 - 1 x -3 = 5

P-1 = $\frac{1}{5}$ $\begin{pmatrix} 1 & 3 \\ -1 & 2 \end{pmatrix}$

= $\begin{pmatrix} {\frac{1}{5}} & {\frac{3}{5}} \\ -{\frac{1}{5}} & {\frac{2}{5}} \end{pmatrix}$

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