Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det(A\)⁻^4A^8A⁻^2A) equals:</p>
<p>(A) 4</p>
<p>(B) 16</p>
<p>(C) 64</p>
<p>(D) 256</p>
Step-by-Step Solution
Key Concept: Exponent sum: -4 + 8 - 2 + 1 = 3 \Rightarrow $A$^3.
1. Expression = $A$^3
2. det(A$^3) = 4^3 = 64
Correct Answer: 3