Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If det(A)=k, then det(\(A\)^T\)\(A) equals:</p>
<p>(A) \(k^2\)</p>
<p>(B) k</p>
<p>(C) 2k</p>
<p>(D) \(k^3\)</p>
Step-by-Step Solution
Key Concept: det(A\)^TA) = det(A\)^T) \times \(\det(A)\) = k \times k = k^2.
1. det(\(A\)^T)=k
2. Multiply \to \(k^2\)
Correct Answer: 1