Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^nA^nA⁻^n) equals:</p>
<p>(A) k^n</p>
<p>(B) k^(2n)</p>
<p>(C) k</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Combine powers: n + n - n = n \Rightarrow $A$^n.
1. Expression = $A$^n
2. det(A$^n)=k^n
Correct Answer: 1