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Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 &...

Given the matrix $A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}$ . Find the inverse of matrix A.

A.

$\begin{vmatrix} 6 & 2 \\ 1 & 6 \end{vmatrix}$

B.

$\begin{vmatrix} \frac{2}{11} & \frac{1}{12}\\ \frac{3}{20} & \frac{1}{10} \end{vmatrix}$

C.

$\begin{vmatrix} -3 & 2 \\ -1 & -6 \end{vmatrix}$

D.

$\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20}\end{vmatrix}$

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Correct answer is D

$A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}$

|A| = (3 x 6) - (-2 x 1)

= 18 + 2

= 20.

A $^{-1}$ = $\frac{1}{20} \begin{vmatrix} 6 & 2 \\ -1 & 3 \end{vmatrix}$

= $\begin{vmatrix} \frac{6}{20} & \frac{2}{20} \\ \frac{-1}{20} & \frac{3}{20} \end{vmatrix}$

= $\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20} \end{vmatrix}$

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