Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^3A⁻^3) equals:</p>
<p>(A) 1</p>
<p>(B) k</p>
<p>(C) k^2</p>
<p>(D) 0</p>
Step-by-Step Solution
Key Concept: Simplify first: $A$^3A⁻^3 = $I$.
1. $A$^3A⁻^3 = $I$
2. det(I)=1
Correct Answer: 1