Show that the Walsh matrix (mathbf{W}) has the property (mathbf{W}_{(m)}^{2}=m mathbf{I}_{(m)}), where each of the matrices is

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Show that the Walsh matrix \(\mathbf{W}\) has the property \(\mathbf{W}_{(m)}^{2}=m \mathbf{I}_{(m)}\), where each of the matrices is of order \(m\).

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