Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)^7A^4A⁻^4A⁻^7A^5) equals:</p>
<p>(A) 5</p>
<p>(B) 25</p>
<p>(C) 125</p>
<p>(D) 3125</p>
Step-by-Step Solution
Key Concept: Exponent sum: 7 + 4 - 4 - 7 + 5 = 5 \Rightarrow $A$^5.
1. Expression = $A$^5
2. det(A$^5)=5^5=3125
Correct Answer: 4