Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=2, then det(A\)⁻^2A^5A⁻^3) equals:</p>
<p>(A) 1</p>
<p>(B) 2</p>
<p>(C) 4</p>
<p>(D) 8</p>
Step-by-Step Solution
Key Concept: Exponent sum: -2 + 5 - 3 = 0 \Rightarrow \(I\).
1. Total exponent = 0
2. Matrix = \(I\)
3. det(I) = 1
Correct Answer: 1