Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^{-1}\(A\)^{-1}\(A\)^4) equals:</p>
<p>(A) k</p>
<p>(B) k^2</p>
<p>(C) k^3</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: Simplify exponent: -3 + 4 = 1 \Rightarrow \(A\).
1. \(A\)⁻^3A^4 = \(A\)
2. \(\det(A)\)=k
Correct Answer: 1