If A, B and C are square matrices of order 3 and det(BC)=2~det(A), then what is the value of det(2A^{-1}BC)?
- A. 16 ✓
- B. 8
- C. 4
- D. 2
Correct Answer: A. 16
Explanation
Using the properties of determinants: det(kA) = k^n det(A), so det(2A^{-1}BC) = 2^3 det(A^{-1}) det(BC) = 8 \cdot \frac{1}{det(A)} \cdot 2det(A) = 16.
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