1. $\overline{A\times A}=\overline{A}$
2. $\overline{B\times B}=\overline{B}$
3. $\overline{\overline{A}\times \overline{B}}=\overline{\overline{A+B}}=A+B$ (Using De-Morgan's law $\overline{A}\times\overline{B}=\overline{A+B}$)
4. $\overline{(A+B)+(A+B)}=\overline{A+B}$ $\Rightarrow$ NOR gate
Option B is correct.