Question

Let $A$ be a $2\times 2$ matrix
Statement 1: $adj(adjA$) $=A$
Statement 2: $|adjA|$ = $\left(|A{|}^{(n-1)}\right)$

• A. Statement 1 is true, Statement 2 is true,Statement 2 is a correct explanation for Statement1
• 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 B Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

We know for a matrix of order n,

$det.\left(adj\right(A\left)\right)=det(A{)}^{n-1}$ and $adj\left(adj\right(A\left)\right)=det(A{)}^{n-2}A$

But Statement 2 does not explain Statement 1

So, Option (B)