Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)⁻^nA^m) where n>m equals:</p>
<p>(A) k^(n-m)</p>
<p>(B) k^(m-n)</p>
<p>(C) 1/k^(n-m)</p>
<p>(D) 1</p>
Step-by-Step Solution
Key Concept: \(A\)⁻^nA^m = \(A\)^(m-n) = \(A\)^-(n-m), so determinant is k^-(n-m).
1. m-n is negative \Rightarrow -(n-m)
2. det = k^-(n-m) = 1/k^(n-m)
Correct Answer: 3