What is an identity exactly? I hear the phrase “Additive Identity” which is something you add to a number that does not change its value. However, if I have 1 + 0 = 1, I assume 0 is the “Additive Identity” and the “Identity” is 1 correct?

Also, I see a reference to the “Identity Matrix” but it seems like this is really the “Multiplicative Identity matrix” correct? Since there is also an Additive Identity Matrix (all zeroes). Does this make sense? And in this case, wouldn’t the “Identity” just be the Matrix itself?

I am just trying to clarify the usage of the terms.