Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det(A\)^5(A\)⁻^5 + \(I)(A\)⁻^5 - \(I)(A\)⁻^5 + \(I)) equals:</p>
<p>(A) 1</p>
<p>(B) 4</p>
<p>(C) cannot be determined</p>
<p>(D) 16</p>
Step-by-Step Solution
Key Concept: Still reduces to subtraction + addition terms.
1. Expression expands
2. Cannot simplify determinant
3. Answer: cannot be determined
Correct Answer: 3