False
If B is an idempotent matrix, it means that B^2 = B.
However, this statement does not guarantee B is either the identity matrix (In) or not invertible.
Idempotent matrices are a special kind of matrix with special properties but it cannot be used to determine invertibility or whether B=In.
If an idempotent matrix B is given, there is no way to determine whether B is In or invertible from this information alone, as many different matrices can be idempotent.