Statement-1: If A and B are two non-singular matrices of the same order, then $adj (AB) = (adj\, B) (adj\, A)$
Statement-2: $A (adj\, A) = |A|I$
Answer & explanation
Correct answer: option 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
$∴adj\, (AB) = (adj\, B) (adj\, A)$