Question

A matrix of order 3X3 has determinant 5. What is the value of |3A|?

Answer 1

$\textsf{Given:}$

$\textsf{If A is a square matrix of order n, then}$

$\mathsf{|kA|=k^n|A|}$

$\textsf{Given:}$

$\textsf{A is a square matrix of order 3 and }\mathsf{|A|=5}$

$\textsf{Then,}$

$\mathsf{|3A|=3^3|A|}$

$\implies\mathsf{|3A|=27|A|}$

$\implies\mathsf{|3A|=27(5)}$

$\implies\boxed{\mathsf{|3A|=135}}$