Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=4, then det((A\)^5A⁻^5)^6) equals:</p>
<p>(A) 1</p>
<p>(B) 4</p>
<p>(C) 16</p>
<p>(D) 4096</p>
Step-by-Step Solution
Key Concept: $A$^5A⁻^5 = $I$ \Rightarrow any power remains $I$.
1. $A$^5A⁻^5 = $I$
2. $I$^6 = $I$
3. det(I)=1
Correct Answer: 1