Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det(A\)^7A^4A⁻^4) equals:</p>
<p>(A) 5</p>
<p>(B) 25</p>
<p>(C) 125</p>
<p>(D) 78125</p>
Step-by-Step Solution
Key Concept: Simplify: 7 + 4 - 4 = 7 \Rightarrow $A$^7.
1. Expression = $A$^7
2. det(A$^7) = 5^7 = 78125
Correct Answer: 4