KCET · Maths · Matrices
If \(A\) and \(B\) are matrices of order 3 and \(|A|=5,|B|=3\), then \(|3 A B|\) is
- A 425
- B 405
- C 565
- D 585
Answer & Solution
Correct Answer
(B) 405
Step-by-step Solution
Detailed explanation
Given order of matrix \(A\) and \(B\) are 3 ,
\(|A|=5,|B|=3\)
\(\Rightarrow\) The order of \(A B\) matrix is also 3 .
\(|A B|=|A| \cdot|B|=15\)
Using the property \(|K A|=K^{n}|A|\), where \(n\) is the order of square matrix
\(\begin{aligned}
\Rightarrow \quad|3 A B| &=3^{3}|A B| \\
&=27 \times 15=405
\end{aligned}\)
\(|A|=5,|B|=3\)
\(\Rightarrow\) The order of \(A B\) matrix is also 3 .
\(|A B|=|A| \cdot|B|=15\)
Using the property \(|K A|=K^{n}|A|\), where \(n\) is the order of square matrix
\(\begin{aligned}
\Rightarrow \quad|3 A B| &=3^{3}|A B| \\
&=27 \times 15=405
\end{aligned}\)
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