Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)⁻^2A^6A⁻^3A) equals:</p>
<p>(A) 3</p>
<p>(B) 9</p>
<p>(C) 27</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Exponent sum: -2 + 6 - 3 + 1 = 2 \Rightarrow $A$^2.
1. Expression = $A$^2
2. det(A$^2) = 3^2 = 9
Correct Answer: 2