Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^n(A\)⁻^n + \(I)(A\)⁻^n - \(I)(A\)⁻^n + \(I)) equals:</p>
<p>(A) k^n</p>
<p>(B) 1</p>
<p>(C) cannot be determined</p>
<p>(D) k</p>
Step-by-Step Solution
Key Concept: Repeated multiplication still leads to expressions involving sums/differences.
1. Combine terms \to involves sums and differences
2. No determinant rule applies
3. Cannot determine
Correct Answer: 3