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Question

Mathematics Question on Matrices

Which one of the following is true always for any two non-singular matrices A and B of same order ?

A

AB=BAAB = BA

B

(AB)t=AtBt(AB)^t = A^t B^t

C

(A+B) (A−B)=A2−B2(A+B)\,(A-B)=A^2-B^2

D

(AB)−1=B−1A−1(AB)^{-1}=B^{-1}A^{-1}

Answer

(AB)−1=B−1A−1(AB)^{-1}=B^{-1}A^{-1}

Explanation

Solution

Answer (d) (AB)−1=B−1A−1(AB)^{-1}=B^{-1}A^{-1}