KCET · Maths · Differential Equations
If \( \mathrm{A} \) is a square matrix of order \( 3 \times 3 \), then \( |\mathrm{KA}| \) is equal to
- A \( |\mathrm{KA}| \)
- B \( \mathrm{K}^{2}|\mathrm{~A}| \)
- C \( \mathrm{K}^{3}|\mathrm{~A}| \)
- D 3K|A|
Answer & Solution
Correct Answer
(C) \( \mathrm{K}^{3}|\mathrm{~A}| \)
Step-by-step Solution
Detailed explanation
Given that, matrix \(A\) of order \(3 \times 3\).
We know that, for a matrix of order \(n \times n\) we have
\(|K A|_{n \times n}=K^{n}|A|\)
Here \(n=3\), we get
\(|K A|_{3 \times 3}=K^{3}|A|\)
We know that, for a matrix of order \(n \times n\) we have
\(|K A|_{n \times n}=K^{n}|A|\)
Here \(n=3\), we get
\(|K A|_{3 \times 3}=K^{3}|A|\)
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