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Let \(\mathbf{A}\) be an invertible square matrix, and let \(\mathbf{X}\) and \(\mathbf{B}\) be matrices of compatible sizes. Prove that if \(\mathbf{A}\mathbf{X} = \mathbf{B}\), then \(\mathbf{X} = \mathbf{A}^{-1}\mathbf{B}\).
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