If A and B are non-singular matrices of order three such that adj(A B)=[1 1 1 1 p 1 1 1 p] and |B2 adj(A)|=p2-3, then p is

Question

If A and B are non-singular matrices of order three such that adj(A B)=[1 1 1 1 p 1 1 1 p] and |B2 adj(A)|=p2-3, then p is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

adj(A B)=|A B|2=(p-1)2 |B2 adj A|=|B2||A|2=|A B|2 ⇒(p-1)2=p2-3 ⇒ p=2

Q. If $A$ and $B$ are non-singular matrices of order three such that $a d j (A B) = ⎣ ⎡ 111 1 p 1 11 p ⎦ ⎤$ and $∣ ∣ B^{2} a d j (A) ∣ ∣ = p^{2} - 3$ , then $p$ is