Statement-1: If A and B are two non-singular matrices of the same order, then $adj (AB) = (adj\, B) (adj\, A)$

Statement-2: $A (adj\, A) = |A|I$

Statement-1 is True, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

We have,

$(AB) (adj\, AB) =|AB| I$ ...(i)  $[∵A (adj\, A) =|A|I]$

$(AB) (adj\, B adj\, A) = A (B\, adj\, B) adj\, A$

$⇒(AB) (adj\, B\, adj\, A)=(A(|B|I)) adj\,A$   $[∵ B (adj\, B) =|B| I]$

$⇒(AB) (adj\, B\, adj\, A) =|B| (A\, adj\, A)$

$⇒(AB) (adj\, B\, adj\, A) =|B||A| I=|AB| I$  ...(ii)

From (i) and (ii), we get

$∴adj\, (AB) = (adj\, B) (adj\, A)$