Haryana Police Constable Model Paper 3

Concept: det $\left({\mathrm{A}}^{\mathrm{T}}\right)$ = det (A)
det (-A) = ( $-1{)}^{\mathrm{n}}$ det (A), where n is the order of the matrix
Calculation:
For a skew symmetric matrix:
A = $-{\mathrm{A}}^{\mathrm{T}}$
Take determinant on both sides,
⇒ det A = det$\left(-{\mathrm{A}}^{\mathrm{T}}\right)$
⇒ det A = det (- A) (∵det $\left({\mathrm{A}}^{\mathrm{T}}\right)$ = det (A))
We know that det (-A) =${\left(-1\right)}^{\mathrm{n}}$ det (A), where n is the order of the matrix
Given order is odd
So, n is odd, let n = 1
Then det A = - det A
2 det A = 0
Thus det A = 0, so option 1 is correct.