Given (mathbf{A}_{n times n}) and scalar (k eq 0), show that ((k mathbf{A})^{-1}=frac{1}{k} mathbf{A}^{-1}).

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Given \(\mathbf{A}_{n \times n}\) and scalar \(k eq 0\), show that \((k \mathbf{A})^{-1}=\frac{1}{k} \mathbf{A}^{-1}\).

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