Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^nA^mA⁻^nA⁻^mA^nA⁻^n) equals:</p>
<p>(A) 1</p>
<p>(B) k^n</p>
<p>(C) k^m</p>
<p>(D) k</p>
Step-by-Step Solution
Key Concept: All powers cancel completely \Rightarrow identity matrix.
1. Sum exponents = 0
2. Matrix = $I$
3. det(I)=1
Correct Answer: 1