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Let \(\mathbf{A}\), \(\mathbf{B}\), and \(\mathbf{C}\) be square matrices of the same order. Suppose that \(\mathbf{A}\) is an invertible matrix. Prove that if \(\mathbf{A}\mathbf{B} = \mathbf{A}\mathbf{C}\), then \(\mathbf{B}=\mathbf{C}\).
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