Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \det(A)=k, then \det(\(A\)^T\)\(A\)^{-1}\)\(A) equals:</p>
<p>(A) k</p>
<p>(B) 1</p>
<p>(C) \(k^2\)</p>
<p>(D) 0</p>
Step-by-Step Solution
Key Concept: Simplify inside first: $A$^{-1}$A$ = $I$ \Rightarrow expression reduces to $A$^T.
1. $A$^{-1}$A$ = $I$
2. Expression becomes $A$^T$
3. \det(A$^T)=\det($A)=k
Correct Answer: 1