If A,B and C arae three non-singular square matrices of order 3 satisfying the equation `A^(2)=A^(-1)` let `B=A^(8) and C=A^(2)` ,find the value of det (B-C)

Explanation

To solve the problem, we need to find the value of \( \det(B - C) \) where \( B = A^8 \) and \( C = A^2 \), given that \( A^2 = A^{-1} \).

### Step-by-Step Solution:

1. **Understanding the given information**:
We know that \( A^2 = A^{-1} \). This means that multiplying \( A \) by itself gives us the inverse of \( A \).

2. **Expressing \( B \) in terms of \( A \)**:
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