If \( \left[\begin{array}{cc}a & b \\ c & 1-a\end{array}\right] \) is an idempotent matrix and \....

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If \( \left[\begin{array}{cc}a & b \\ c & 1-a\end{array}\right] \) is an idempotent matrix and \( f(x)=x-x^{2} \) and \( b c=\frac{1}{4} \), then the value of \( 4 f(a) \)
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