Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^n(A\)⁻^n - \(I)) equals:</p>
<p>(A) k^n - 1</p>
<p>(B) 1 - k^n</p>
<p>(C) cannot be determined</p>
<p>(D) k^n</p>
Step-by-Step Solution
Key Concept: Subtraction inside determinant behaves same as addition—no simplification possible.
1. Expression includes subtraction
2. No determinant rule applies
3. Cannot determine
Correct Answer: 3