Chapter 2 - Matrices and Systems of Linear Equations - 2.8 The Invertible Matrix Theorem I - Problems - Page 189: 1

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Let $A$ = invertible matrix and $B,C$ are matrices of the same size as $A$ such as $$AB=AC$$ then $$AB-AC=0$$ $$\rightarrow A(B-C)=0$$ (By Theorem 2.2.18) The only solution of the equation is $$B-C=0$$ (By part (c) of the Invertible Matrix Theorem) $$B=C$$