#### provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise  Fill in the blanks question 2

Answer: $\left | A \right |=0$

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

Given: A is $3\times 3$ order skew symmetric matrix

Solution: Here, $A_{\left [ 3\times 3 \right ]}$ and $A=-A^{T}$ ( Skew Symmetric )

So,  $A=-A^{T}$

$\left | A \right |=-\left | A^{T} \right |$           [Taking determinant both side]

$\left | A \right |=-\left | A \right |\; \; \; \; \; \; \; \;$                $\left [ \left | A^{T} \right |=\left | A \right | \right ]$

$\left | A \right |+\left | A \right |=0$

$2\left | A \right |=0$

$\left | A \right |=0$

So, here determinant of 3 $3\times 3$ skew symmetric matrix always be zero.