Given A = $\begin{bmatrix} 2 & -3 \\ -4 & 7 \end{bmatrix}$ |A| = 2 × - [(- 4) × (- 3)] = 2 ⇒ $A^{-1}$ exist. Cofactors of matrix A are $C_{11}$ = 7 , $C_{12}$ = - 4 , $C_{21}$ = - 3 , $C_{22}$ = 2 Minors of matrix A are $M_{11}$ = $(-1)^{1+1}$ × 7 = 7 $M_{12}$ = $(-1)^{1+2}$ × (- 4) = 4 $M_{21}$ = $(-1)^{3+1}$ × (- 3) = 3 $M_{22}$ = $(-1)^{2+2}$ × 2 = 2 $A^{-1}$ = $\frac{1}{2} \begin{pmatrix} 7 & 3 \\ 4 & 2 \end{pmatrix}$ 2 $A^{-1}$ = $\begin{pmatrix} 7 & 3 \\ 4 & 2 \end{pmatrix}$ ... (i) 9I - A = 9 $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} - \begin{pmatrix} 2 & -3 \\ -4 & 7 \end{pmatrix}$ = $\begin{pmatrix} 7 & 3 \\ 4 & 2 \end{pmatrix}$ ... (ii) ⇒ $2X^{-1}$ = 9I - A from (i) and (ii)