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Let $E$ be a square matrix with all but one entry equal to $0$. Suppose the nonzero entry is $b$ and that it is found in row $i$, column $j$.

In which of the following cases will $E$ be an idempotent matrix?

$i=j$ and $b=1$

$i=j$ and $b=-1$

$i=j$ and $b=2$

$i\neq j$ and $b=1$

$i\neq j$ and $b=-1$

$i\neq j$ and $b=2$