Question

A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.

Answer 1

Let A be the given matrix . Then, 
\[\left| A \right| = 2 \left[\text{ Order }= n = 3 \right] \] 
\[\left| I \right| = 1 \left[\text{ I is an identity matrix }\right]\] 
\[3\left( I \right) = 3\] 
\[\left| A3\left( I \right) \right| = \left| 3A \right| = 3^3 \left| A \right| \left[\text{ A being of order 3 }\right]\] 
\[ = 27 \times 2 = 54\] 
\[ \Rightarrow \left| A3\left( I \right) \right| = 54\]