Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^5A^2A⁻^2) equals:</p>
<p>(A) 3</p>
<p>(B) 9</p>
<p>(C) 27</p>
<p>(D) 243</p>
Step-by-Step Solution
Key Concept: Simplify: 5 + 2 - 2 = 5 \Rightarrow $A$^5.
1. Expression = $A$^5
2. det(A$^5) = 3^5 = 243
Correct Answer: 4