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

Answer: $\partial =\pm 3$

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

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

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

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

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

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

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

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

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

From equation (1) and equation (2)

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

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

$\inline \partial ^{2}=9$

$\inline \partial=\pm 3$