Question

Statement - 1: $A=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$, then $adj\left(adjA\right)=A$
Statement - 2 : If A is a square matrix of order n, then $adj\left(adjA\right)={\left|A\right|}^{n-2}A$

• A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
• B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
• C. Statement-1 is True, Statement-2 is False.
• D. Statement-1 is False, Statement-2 is True.

Answer 1

The correct option is A Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

Given, $A=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$
$adjA=C^T=\left[\begin{array}{ccc}1& -1& 0\\ -2& 3& -4\\ -2& 3& -3\end{array}\right]$
Now, $adj\left(adjA\right)={\left[\begin{array}{ccc}3& 2& 0\\ -3& -3& -1\\ 4& 4& 1\end{array}\right]}^T$
$\Rightarrow adj\left(adjA\right)=\left[\begin{array}{ccc}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$
$\Rightarrow adj\left(adjA\right)=A$
Also, we know that $adj\left(adjA\right)=|A{|}^{n-2}A$