Chapter 2 - Matrices and Systems of Linear Equations - 2.6 The Inverse of a Square Matrix - Problems - Page 178: 40

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$A, B, C$ are $n \times n$ matrices satisfying $B A = I_n$ and $CA = I_n$ According to Theorem 2.6.11 we have $A,B,C$ are invertibleand $A=B^{-1}$ and $A=C^{-1}$ We have $A^{-1} = (B^{-1})^{-1}=B$ and $A^{-1} = (C^{-1})^{-1}=C$ Therefore, $B=C$