Question

Let $A$ be a 2 x 2 matrix Statement-1: adj $\left(adjA\right)=A$ Statement 2 :$\left|adjA\right|=\left|A\right|$ Select the correct choice:

• A. Statement 1is true, Statement2 is true; Statement-2 is not a.correct explanation for Statement 1
• B. Statement-1 is true, Statement-2 is false
• C. Statement 1 is false, Statement-2 is true
• D. Statement 1is true, Statement-2 is true; Statemerit-2 is correct explanation for Statement-1

Answer 1

Answer: (A)

Statement 1is true, Statement2 is true; Statement-2 is not a.correct explanation for Statement 1

We have $adj\left(adjA\right)={\left|A\right|}^{n-2}A$
Here $n=2$ which gives adj $\left(adjA\right)=A$
Hence, statement 1 is true.
Again $\left|adjA\right|={\left|A\right|}^{n-1}$
Here $n=2$ which give $\left|adjA\right|=\left|A\right|$
Thus statement-2 is also true. But statement-2 doesn't explain statement 1