Q. 40

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

B.A-1B

C.A-1B-1

D.B-1A-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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