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IMC
2009 IMC
2
IMC 2009 Day 1 P2
IMC 2009 Day 1 P2
Source:
July 15, 2014
IMC
college contests
Problem Statement
Let
A
,
B
,
C
A,B,C
A
,
B
,
C
be real square matrices of the same order, and suppose
A
A
A
is invertible. Prove that
(
A
−
B
)
C
=
B
A
−
1
⟹
C
(
A
−
B
)
=
A
−
1
B
(A-B)C=BA^{-1}\implies C(A-B)=A^{-1}B
(
A
−
B
)
C
=
B
A
−
1
⟹
C
(
A
−
B
)
=
A
−
1
B
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