Question

If A is a square matrix of order 3 with determinant 4, then write the value of |−A|.

Answer 1

$$\begin{gathered} \left|A\right|=4 \\ \mathrm{Here}, \\ \mathrm{Order}\mathrm{of}\mathrm{the}\mathrm{matrix}\left(n\right)=3 \\ \mathrm{Using}\mathrm{properties}\mathrm{of}\mathrm{matrices},\mathrm{we}\mathrm{get} \\ \left|\mathrm{kA}\right|={\mathrm{k}}^{\mathrm{n}}\left|\mathrm{A}\right|\left[\mathrm{For}\mathrm{a}\mathrm{square}\mathrm{matrix}\mathrm{o}\mathrm{f}\mathrm{order}n\mathrm{and}\mathrm{constant}k\right] \\ \Rightarrow \left|-\mathrm{A}\right|={\left(-1\right)}^3\left|\mathrm{A}\right|=\left(-1\right)\times 4=-4 \end{gathered}$$