Question

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

 

Answer 1

\[\text{ If }A = \left[ a_{i j} \right]\text{ is a square matrix of order n and k is a constant, then}\] 
\[\left| kA \right| = k^n \left| A \right| \] 
Here, 
Number of rows = n 
k is a common factor from each row of k
\[\left| 3A \right| = 3^3 \left| A \right| = 27 \times 5 = 135 \left[\text{ Given matrix is 3 }\times\text{ 3 such that }\left| A \right| = 5 \right]\] 
\[\text{ Thus,} \left| 3A \right| = 135\]