#### Please Solve RD Sharma Class 12 Chapter 6 Adjoint and Inverse of a Matrix  Exercise fill in the blaks Question 18 Maths Textbook Solution.

Answer    $\rightarrow \frac{1}{9}\left[\begin{array}{ll} 0 & 3 \\ 3 & 1 \end{array}\right]$

Given   $\rightarrow A=\left[a_{i j}\right]_{2 \times 2} \text { where } a_{i j}=\left\{i+j \text { if } i \neq j i^{2}-2 j \text { if } i=j\right.$

Hint  $\rightarrow A^{-1}=\frac{1}{|A|} \operatorname{adj} A$

Explanation $\rightarrow$ find $a_{11}, a_{12}, a_{21}, a_{22}$

\begin{aligned} &a_{11}=1^{2}-2 \times 1=-1 \\ &a_{12}=1+2=3 \\ &a_{21}=2+1=3 \\ &a_{22}=2^{2}-2 \times 2=0 \\ &A=\left[\begin{array}{cc} -1 & 3 \\ 3 & 0 \end{array}\right] \end{aligned}

\begin{aligned} &|A|=-1 \times 0-3 \times 3=-9 \\ &\operatorname{adj} A=\left[\begin{array}{cc} 0 & -3 \\ -3 & -1 \end{array}\right] \\ &A^{-1}=\frac{1}{-9}\left[\begin{array}{cc} 0 & -3 \\ -3 & -1 \end{array}\right] \end{aligned}

$A^{-1}=\frac{1}{9}\left[\begin{array}{ll} 0 & 3 \\ 3 & 1 \end{array}\right]$