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