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### Answers (1)

Answer:8

Hint: Here we use basic concept of identity matrix and determinant of matrix

Given:

$A \text { is }\left[a_{i j}\right] \text { is } 3 \times 3 \text { scalar matrix }$

$a_{11}=2 \text { then write the value of } \left | A \right |$

Solution :

In scalar matrix diagonal entries are same

$a_{11}=a_{22}=a_{33}$

So,

$\left[\begin{array}{ccc} a_{11} & 0 & 0 \\ 0 & a_{22} & 0 \\ 0 & 0 & a_{33} \end{array}\right]=\left[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right]$

$\rightarrow$ Lets find determinate

\begin{aligned} &|A|=\left|\begin{array}{lll} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right| \\ &=2\left|\begin{array}{ll} 2 & 0 \\ 0 & 2 \end{array}\right|-0\left|\begin{array}{ll} 0 & 0 \\ 0 & 2 \end{array}\right|+0\left|\begin{array}{ll} 0 & 2 \\ 0 & 0 \end{array}\right| \\ &=2(4-0)-0(0-6)+0(0-0) \\ &=2(4)=8 \\ &|A|=8 \end{aligned}

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