Question

Statement - 1 : If $A$ is a non $-$ singular square matrix of order $n$, then $\left|adjA\right|={\left|A\right|}^{n-1}$
Statement - 2 : For any square matrix $A$ of order $n$, $A\left(adjA\right)=\left|A\right|$ I and $\left|kA\right|=k\left|A\right|$

• 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 C Statement-1 is True, Statement-2 is False.

By property of adjoint of matrix,
$|adjA|=|A{|}^{n-1}$ where n is order of matrix.
Statement 1 is true.
Also, $adjA=|A|I_n$ where n is order of matrix
$|kA|=k^n|A|$ where n is order of matrix
Hence, statement 2 is incorrect