Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^4(I\) - \(A\)⁻^4)(I\) + \(A\)⁻^4)(I\) - \(A\)⁻^4)) equals:</p>
<p>(A) 1</p>
<p>(B) 3</p>
<p>(C) cannot be determined</p>
<p>(D) 9</p>
Step-by-Step Solution
Key Concept: Algebraic identity reduces expression but determinant still unknown.
1. Simplify expression
2. Final form contains subtraction
3. Cannot determine
Correct Answer: 3