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^(3n)</p>
<p>(D) k^3</p>
Step-by-Step Solution
Key Concept: Add exponents: n + n + n = 3n \Rightarrow $A$^(3n).
1. Expression = $A$^(3n)
2. det = k^(3n)
Correct Answer: 3