Question

If A = [a_ij] is a 3 × 3 scalar matrix such that a₁₁ = 2, then write the value of |A|.

Answer 1

A scalar matrix is a diagonal matrix, in which all the diagonal elements are equal to a given scalar number.

$$\begin{gathered} \mathrm{Given}:\mathrm{A}=\left[a_{ij}\right]\mathrm{is}3\times 3\mathrm{matrix},\mathrm{where}{a}_{11}=2 \\ \Rightarrow \mathrm{A}=\left[200 \\ 020 \\ 002\right] \\ \Rightarrow \left|\mathrm{A}\right|=\left|200 \\ 020 \\ 002\right| \\ =2\times \left|20 \\ 02\right|\left[\mathrm{Expanding}\mathrm{along}{\mathrm{C}}_1\right] \\ =2\times 2\times 2=8 \end{gathered}$$