Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det(A\)^4A^2A⁻^5A^{-1}) equals:</p>
<p>(A) 1</p>
<p>(B) 4</p>
<p>(C) 16</p>
<p>(D) 64</p>
Step-by-Step Solution
Key Concept: Exponent sum: 4 + 2 - 5 - 1 = 0 \Rightarrow $I$.
1. Expression = $I$
2. det(I)=1
Correct Answer: 1