Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)^6A⁻^6A^4) equals:</p>
<p>(A) 5</p>
<p>(B) 25</p>
<p>(C) 125</p>
<p>(D) 625</p>
Step-by-Step Solution
Key Concept: Exponent sum: 6 - 6 + 4 = 4 \Rightarrow $A$^4.
1. Expression = $A$^4
2. det(A$^4) = 5^4 = 625
Correct Answer: 4