Question

Let A be a 2 × 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 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-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

Answer 1

(a) : We have adj(adj A) = |A|^n–2A
Here n = 2, which gives adj(adj A) = A
The statement-1 is true.
Again |adj A| = |A|^{n – 1}
Here n = 2, which gives |adj A| = |A|
Thus statement-2 is also true. But statement-2 doesn’t explain statement-1.