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

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