Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=5, then det((A\)^6A⁻^6)^7) equals:</p>
<p>(A) 1</p>
<p>(B) 5</p>
<p>(C) 25</p>
<p>(D) 78125</p>
Step-by-Step Solution
Key Concept: $A$^6A⁻^6 = $I$ \Rightarrow determinant = 1.
1. $A$^6A⁻^6 = $I$
2. $I$^7 = $I$
3. det(I)=1
Correct Answer: 1