Question

A and B are two invertable matrix of same order then (Ab)-1is equal to​

Answer 1

Step-by-step explanation:

If X,Y are two matrices

XY=YX=I

Then X=Y

−1

Given B −1A −1 =(AB) −1

Multiply with AB to B −1 A −1

ABB −1 A −1 =A(BB −1 )A

Multiply with B −1 A −1 to AB B −1 A −1 AB=B −1 IB=B−1B=IAB(B −1 A −1 )=(B −1 A −1 )AB=I

(AB) −1 =B −1 A −1

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