Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^n(A\)⁻^n + \(I)^3) equals:</p>
<p>(A) 1</p>
<p>(B) k^n</p>
<p>(C) cannot be determined</p>
<p>(D) k^3</p>
Step-by-Step Solution
Key Concept: Even higher powers of a sum still cannot be simplified under determinant.
1. Expression contains (A$⁻^n + $I)^3
2. No determinant rule applies
3. Cannot determine
Correct Answer: 3