Matrices & Determinants
Inverse of a matrix
Grade 12
Question:
<p>If \det(A) = 3, then \det(k\(A\)^{-1}) for \(3 \times 3\) matrix is:</p>
<p>(A) \(k^3\)/3</p>
<p>(B) \(k^3\)/27</p>
<p>(C) k/3</p>
<p>(D) \(k^3\)/9</p>
Step-by-Step Solution
Key Concept: det(kA^{-1}) = k^3 \times det(A\)^{-1}) = k^3 / \(\det(A)\).
1. \(\\(\det(A)\)^{-1})=1/3
2. \det(k\(A\)^{-1})=\(k^3\) \times (1/3)
3. = \(k^3\)/3
Correct Answer: 1