Question

If |A| denotes the value of the determinant of a square matrix of order 3, then |–2A| = ___________.

Answer 1

Given:
A is a 3 × 3 matrix


$$\begin{gathered} \mathrm{Now}, \\ \left|-2A\right|={\left(-2\right)}^3\left|A\right|\left(\because \mathrm{Order}\mathrm{of}A\mathrm{is}3\times 3\right) \\ =-8\left|A\right| \end{gathered}$$

Hence, |–2A| = –8|A|.