Let $p$ be a prime number. Let $J$ be the set of all $2 \times 2$ matrices $\binom{c b}{c d}$ whose entries are chosen from $\{0,1,2, \cdots, p-1\}$ and satisfy the conditions $a+d \equiv 1(\bmod p), a d-b c \equiv 0(\bmod p)$. Determine how many members $J$ has. Please provide the number of members when $p=2$. 

Let's think step by step and output the final answer within \boxed{}.
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