Let A and B be two invertible square matrices of same order, then which of the following is not correct ?
Answer & explanation
Correct answer: option 4
Check each option.
(1) $(AB)^{-1}=B^{-1}A^{-1}$ is a standard property of inverse matrices → correct.
(2) $(AB)^{T}=B^{T}A^{T}$ is a standard property of transpose → correct.
(3) If $A^{T}=-A$, then $A$ is skew-symmetric → correct (definition).
(4) Multiplication of matrices is not commutative in general, i.e., $AB\ne BA$ → incorrect.
final answer: Multiplication of A and B is always commutative