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