Q: Does "rub" have the same meaning in the following two sentences?

Rub my hands.

The cat rubbed itself against my leg.

A: the same meaning

Q: Does "identity" have the same meaning in the following two sentences?

Simply an identity element if both are true.

A left identity if I * x = x for any x in the structure.

A: the same meaning

Q: Does "size" have the same meaning in the following two sentences?

The only city of any size in that area.

He blanched when he saw the size of the bill.

A:
the same meaning