Question

The reciprocal matrix of $\left[\begin{array}{ccc}1& 0& 2\\ 0& 1& -1\\ 1& 2& 1\end{array}\right]$ is

• A. $\left[\begin{array}{ccc}-3& -4& 2\\ -1& 1& -1\\ 1& 2& -1\end{array}\right]$
• B. $\left[\begin{array}{ccc}3& 4& -2\\ 1& -1& 1\\ -1& -2& 1\end{array}\right]$
• C. $\left[\begin{array}{ccc}-3& -1& 1\\ -4& 1& 2\\ 2& -1& -1\end{array}\right]$
• D. $\left[\begin{array}{ccc}3& 4& -2\\ -1& -1& 1\\ -1& -2& 1\end{array}\right]$

Answer 1

Answer: (D)

$\left[\begin{array}{ccc}3& 4& -2\\ -1& -1& 1\\ -1& -2& 1\end{array}\right]$

Given matrix is $\left[\begin{array}{ccc}1& 0& 2\\ 0& 1& -1\\ 1& 2& 1\end{array}\right]$
$|A|=1$
cofactor matrix is $\left[\begin{array}{ccc}3& -1& -1\\ 4& -1& -2\\ -2& 1& 1\end{array}\right]$
$adjA=\left[\begin{array}{ccc}3& 4& -2\\ -1& -1& 1\\ -1& -2& 1\end{array}\right]$
$\therefore A^{-1}=\left[\begin{array}{ccc}3& 4& -2\\ -1& -1& 1\\ -1& -2& 1\end{array}\right]$