Matrices & Determinants
Inverse of a matrix
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^nA⁻^n) equals:</p>
<p>(A) 1/k</p>
<p>(B) k</p>
<p>(C) 1</p>
<p>(D) k^2</p>
Step-by-Step Solution
Key Concept: Simplify: $A$^nA⁻^n = $I$ \Rightarrow expression reduces to $A$^{-1}.
1. $A$^nA⁻^n = $I$
2. Expression = $A$^{-1}
3. det(A$^{-1}) = 1/k
Correct Answer: 1