#### provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 14

Hint: Here, we use basic concept of diagonal matrix and determinant of matrix

Given$A= diag(2,34)$

Solution:  $diag(2,34)$

$\text { So, } A=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{array}\right]$

Let’s find determinant of A

\begin{aligned} &|A|=2\left[\begin{array}{ll} 3 & 0 \\ 0 & 4 \end{array}\right]-0\left[\begin{array}{ll} 0 & 4 \\ 0 & 0 \end{array}\right]+0\left[\begin{array}{ll} 0 & 3 \\ 0 & 0 \end{array}\right] \\ &=2(12-0)-0(0-0)+0(0-0) \\ &=2(12)-0+0 \\ &|A|=24 \end{aligned}

So,

\begin{aligned} &\left|A^{2}\right|=|A|^{2}=(24)^{2} \\ &\left|A^{2}\right|=576 \end{aligned}

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