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explain solution RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 8 maths

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Answer: $\partial =\pm 3$

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

Given: $\left | A \right |^{3}=125$ , $A=\begin{bmatrix} \partial & 2\\ 2& \partial \end{bmatrix}$

Solution: Here, $A=\begin{bmatrix} \partial & 2\\ 2& \partial \end{bmatrix}$

So, $\left | A \right |=\partial \times \partial -2\times 2$

$\left | A \right |=\partial^{2} -4$ ........ $(1)$

And, $\left | A \right |^{3}=125$

$\left ( \left | A \right | \right )^{3}=125$

$\left ( \left | A \right | \right )^{3}=(5)^{3}$

$\left | A \right |=5$ ........... $(2)$

From equation (1) and equation (2)

$\partial ^{2}-4=5$

$\partial ^{2}=4+5$

$\partial ^{2}=9$

$\partial=\pm 3$

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