Matrices & Determinants
General
Grade 12
Question:
If $A$ is a square matrix of order $n \times n$ and $k$ is a scalar, then $adj(kA)$ is equal to
$k \text{ adj } A$
$k^n \text{ adj } A$
$k^{n-1} \text{ adj } A$
$k^{n+1} \text{ adj } A$
Step-by-Step Solution
Key Concept: General
<div>$kA \text{ adj } (kA) = |kA|I_n$<br>$\Rightarrow kA \text{ adj } (kA) = k^n |A|I_n$<br>$\Rightarrow kA \text{ adj } (kA) = k^n A \text{ adj } A$<br>Pre-multiplying $A^{-1}$<br>$\Rightarrow \text{ adj } (kA) = k^{n-1} \text{ adj } A$</div>
Correct Answer: C