if A and B are invertible matrices of the same order then prove that (AB)-1=B-1A-1
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Answer:
oh so we have to prove
Explanation:
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
(AB)
−1
=B
−1
A
−1
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