Question

Let $A$ be a $2 \times 2$ matrix Statement-1 : adj (adj A) $= A$ Statement-2 : $|adj \,A| = |A|$

• 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

Answer: (B)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Answer 2

$\left|adj\,A\right|=\left|A\right|^{n-1}=\left|A\right|^{2-1}=\left|A\right|$ $adj\left(adj\,A\right)=\left|A\right|^{n-2}\,A=\left|A\right|^{0}\,A=A$