If $A$ and $B$ are non singular square matrices of the same order, then which of the statements are true?
(A) $(adj A)(adj B)=(adj B)(adj A)$
(B) $(AB)^{T}=A^{T} B^{T}$, if $A^{T}$ denotes transpose of $A$
(C) $(AB)^{-1}=B^{-1} A^{-1}$
(D) Multiplication of matrices is not commutative
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
(A) (adj A)(adj B) = (adj B)(adj A)
This is false as matrix multiplication is not commutative.
(B) $(A B)^{T}=A^{T} B^{T}$, this is false as $(A B)^{T}=B^{T} A^{T}$
(C) → This is true
(D) → This no true