Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^3A^2A⁻^4A^{-1}) equals:</p>
<p>(A) 1</p>
<p>(B) 3</p>
<p>(C) 9</p>
<p>(D) 27</p>
Step-by-Step Solution
Key Concept: Exponent sum: 3 + 2 - 4 - 1 = 0 \Rightarrow \(I\).
1. Expression = \(I\)
2. det(I)=1
Correct Answer: 1