If \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are three non-...

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If \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are three non-singular square matrices of order \(3\) satisfying the equation \( \mathrm{A}^{2}=\mathrm{A}^{-1} \) and let \( B=A^{8} \) and \( C=A^{2} \), find the value of \( \operatorname{det}(B-C) \)
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