|8. Let A and B be invertible matrices of same order n. Does (A + B) exists? If not, show by anexample,​

X,Y are two matrices

XY=YX=I

Then X=Y

−1

Given B

−1

A

−1

=(AB)

−1

Multiply with AB to B

−1

A

−1

ABB

−1

A

−1

=A(BB

−1

)A

−1

=AA

−1

=I

Multiply with B

−1

A

−1

to AB

B

−1

A

−1

AB=B

−1

IB=B

−1

B=I

AB(B

−1

A

−1

)=(B

−1

A

−1

)AB=I