Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\det(A)\)=k, then det(A\)^{-1}\(A\)^TA) 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 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