Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det(A\)^6A^3A⁻^3A⁻^6A^4) 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: 6 + 3 - 3 - 6 + 4 = 4 \Rightarrow $A$^4.
1. Expression = $A$^4
2. det(A$^4) = 4^4 = 256
Correct Answer: 4