Question

Inverse matrix of $ \left[ \begin{matrix} 4 & 7 \\ 1 & 2 \\ \end{matrix} \right] $ is equal to:

• A. $ \left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right] $
• B. $ \left[ \begin{matrix} 2 & -1 \\ -7 & 4 \\ \end{matrix} \right] $
• C. $ \left[ \begin{matrix} -2 & 7 \\ 1 & -4 \\ \end{matrix} \right] $
• D. $ \left[ \begin{matrix} -2 & 1 \\ 7 & -4 \\ \end{matrix} \right] $

Answer 1

Answer: (A)

Let $ A= \begin{bmatrix} 4 & 7 \\ 1 & 2 \\ \end{bmatrix} $
$ |A|=8-7=1 $
Cofactors of $ A $ are $ C_{11}=2,\,\,C_{12}=-1 $
$ C_{21}=-7,\,\,C_{22}=4 $
$ \therefore adj\,\,(A)= \begin{bmatrix} 2 & -7 \\ -1 & 4 \\ \end{bmatrix} $
$ \therefore A^{-1}=\frac{adj\,\,(A)}{|A|}=\frac{1}{1} \begin{bmatrix} 2 & -7 \\ -1 & 4 \\ \end{bmatrix} $
If a matrix, $ A= \begin{bmatrix} a & b \\ c & d \\ \end{bmatrix} $,
then $ adj\,\,(A)= \begin{bmatrix} d & -b \\ -c & a \\ \end{bmatrix} $ .