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