Question

If A is a 2 × 2 matrix such that |A| =5, then |5A| = ___________.

Answer 1

Given:
A is a 2 × 2 matrix
|A| = 5


$$\begin{gathered} \mathrm{Now}, \\ \left|5A\right|=5^2\left|A\right|\left(\because \mathrm{Order}\mathrm{of}A\mathrm{is}2\times 2\right) \\ =25\left|A\right| \\ =25\times 5\left(\because \left|A\right|=5\right) \\ =125 \end{gathered}$$

Hence, |5A| = 125.