In addition operation there is only one additive identity that is zero. The only difference in various applications of this identity lies in the representation - like in matrices, we write it as zero matrix, having all elements equal to zero and in number addition, simply as zero.

According to the additive identity, if M is any expression or number or matrix etc., then,

**M + 0 = M**

Also, the additive identity is commutative as addition is commutative so we can rewrite it as:

**M + 0 = 0 + M = M**

We can also derive the additive inverse using this, The additive inverse of a number is such that when added to given number gives the additive identity.

That is, if a + b = 0, this implies that b is the additive inverse of ‘a’ and vice versa.