Q. 26

If A and B are invertible matrices of the same order then (AB)-1=?
A. (A-1 х B-1)

B. (A х B-1)

C. (A-1 х B)

D. (B-1 х A-1)

Answer :

(AB)(AB)-1 = I

A-1(AB)(AB)-1 = IA-1


(A-1A)B (AB)-1=A-1


IB(AB)-1 = A-1


B(AB)-1 = A-1


B-1B(AB)-1 = B-1 A-1


I (AB)-1 = B-1A-1


(AB)-1 = B-1A-1

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