Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)^6(I\) - \(A\)⁻^6)(I\) + \(A\)⁻^6)(I\) - \(A\)⁻^6)) equals:</p>
<p>(A) 1</p>
<p>(B) 5</p>
<p>(C) cannot be determined</p>
<p>(D) 25</p>
Step-by-Step Solution
Key Concept: Expression simplifies but determinant remains indeterminate.
1. Simplify using identities
2. Contains subtraction
3. Cannot determine
Correct Answer: 3