Let A be a 2 2 matrix Statement-1: adj(adj A )= A Statement-2 : |… - Vidyadip

MCQ

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

A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
✓
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

Correct option: B.

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

(B) $|\operatorname{adj} A |=| A |^{ n -1}=| A |^{2-1}=| A |$
…[Using Shortcut 4(viii)]
$\operatorname{adj}(\operatorname{adj} A )=| A |^{ n -2} A=| A |^0 A= A$
...[Using Shortcut 4(xiii)]
$\therefore$ option (B) is the correct answer.

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