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