Answer
See answer below
Work Step by Step
$A, B, C$ are $n \times n$ matrices satisfying $B A = I_n$ and $AC = I_n$
Multiplying both sides of $B A = I_n$ by $C$:
$(B A)C = I_nC$
We have $(B A)C = B(AC)=BI_n=B$
and $I_nC=C$
Then $B=C$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 2 - Matrices and Systems of Linear Equations - 2.6 The Inverse of a Square Matrix - Problems - Page 178: 39
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