Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=3, then det(A\)^5A^2A⁻^2A⁻^5A^3A⁻^3) 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 = 0 \Rightarrow identity matrix.
1. All exponents cancel
2. Matrix = $I$
3. det(I)=1
Correct Answer: 1