Question

If $A=\left[a_{ij}\right]$ is a 3 × 3 diagonal matrix such that a₁₁ = 1, a₂₂ = 2 a₃₃ = 3, then find |A|.

Answer 1

$$\begin{gathered} \mathrm{If}A=\left[{\mathrm{a}}_{\mathrm{ij}}\right]\mathrm{is}\mathrm{a}\mathrm{diagonal}\mathrm{matrix}\mathrm{of}\mathrm{order}\mathbf{}\mathrm{n},\mathit{}\mathrm{then}\left|A\right|={\mathrm{a}}_{11}\times {\mathrm{a}}_{22}\times {\mathrm{a}}_{33}\times ...\times {\mathrm{a}}_{\mathrm{nn}}. \\ \mathrm{Given}:a_{11}=1,{\mathrm{a}}_{22}=2\mathrm{and}{\mathrm{a}}_{33}=3 \\ \Rightarrow \left|A\right|=1\times 2\times 3=6\left[\mathrm{Applying}\mathrm{the}\mathrm{above}\mathrm{property}\right] \end{gathered}$$