First slide

Applications of determinant

Question

Let A be a 2x2 matrix.
Statement-1: adj(adj A) = A
Statement-2: |adj A| = |A|

Moderate

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

Solution

Let $A = [\begin{array}{ll} a b \\ c d \end{array}]$ then $adj A = [\begin{array}{cc} d & - b \\ - c & a \end{array}]$
$\Rightarrow adj (adj A) = [\begin{array}{ll} a b \\ c d \end{array}] = A$
$∴$ Statement-1 is true.
Also, $| a d j A | = a d - b c = | A |$
$∴$ Statement-2 is true
But statement-2 is not a correct explanation for statement-1.

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