If A = [aij] is a 3 × 3 scalar matrix

Question:

If $A=\left[a_{i j}\right]$ is a $3 \times 3$ scalar matrix such that $a_{11}=2$, then write the value of $|A|$.

Solution:

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

Given: $\mathrm{A}=\left[a_{i j}\right]$ is $3 \times 3$ matrix, where $a_{11}=2$

$\Rightarrow \mathrm{A}=\left[\begin{array}{lll}2 & 0 & 0\end{array}\right.$

$\begin{array}{lll}0 & 2 & 0\end{array}$

$\left.\begin{array}{lll}0 & 0 & 2\end{array}\right]$

$\Rightarrow|\mathrm{A}|=\mid \begin{array}{lll}2 & 0 & 0\end{array}$

$\begin{array}{lll}0 & 2 & 0\end{array}$

$\begin{array}{lll}0 & 0 & 2\end{array}$

$=2 \times \mid \begin{array}{ll}2 & 0\end{array}$

$\begin{array}{ll}0 & 2\end{array}$

[Expanding along $\mathrm{C}_{1}$ ]

$=2 \times 2 \times 2=8$

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