CUET Preparation Today
Let A and B be two invertible square matrices of same order, then which of the following is not correct ? |
$(AB)^{-1}=B^{-1}A^{-1}$ $(AB)^T=B^TA^T, $ where T stands for transpose If $A^T=-A,$ then A is a skew-symmetric matrix Multiplication of A and B is always commutative |
Multiplication of A and B is always commutative |
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 |
