In a ring with 1, an ideal which contains 1 is the entire ring

Let R be a ring with 1 and let I \subseteq R be an ideal. Show that if 1 \in I, then I = R.


Recall that if a \in R and b \in I, then ab \in I. Letting a be arbitrary and b = 1, then, we have R \subseteq I. Hence R = I.

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