$\mathrm{Assertion} \left(\mathrm{A}\right) :\left|\begin{array}{ccc}0& \mathrm{p}-\mathrm{e}& \mathrm{e}-\mathrm{r}\\ \mathrm{e}-\mathrm{p}& 0& \mathrm{r}-\mathrm{p}\\ \mathrm{r}-\mathrm{e}& \mathrm{p}-\mathrm{r}& 0\end{array}\right|=0$

Reason (R) : The determinant of a skew symmetric matrix of odd order is zero.

Both A and R are true and R is the correct explanation of A.

$$\begin{gathered} \mathrm{A}=-{\mathrm{A}}^{\mathrm{T}} \\ \det \mathrm{A}=\det \left(-{\mathrm{A}}^{\mathrm{T}}\right) \\ \det \mathrm{A}=\det (-\mathrm{A}) \\ \det \mathrm{A}=(-1{)}^{\mathrm{n}}\det \mathrm{A}\text{, where }\mathrm{n}\text{ is the order of the matrix. } \\ \text{ if }\mathrm{n}\text{ is odd , let }\mathrm{n}=1 \\ \text{ then }\det \mathrm{A}=-\det \mathrm{A} \\ 2\det \mathrm{A}=0 \\ \det \mathrm{A}=0 \end{gathered}$$