Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^n(I\) - \(A\)⁻^n)(I\) + \(A\)⁻^n)(I\) - \(A\)⁻^n)(I\) + \(A\)⁻^n)) 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 identities still result in difference terms.
1. Combine terms using identities
2. Expression still involves subtraction
3. Cannot determine determinant
Correct Answer: 3