The identity property of addition states that when zero is added to any real number, the number does not change. Thus, the number "0" is called the additive identity for real numbers.
There is a matrix which is an additive identity for matrices:
. |
+ = |
The identity property of multiplication states that when 1 is multiplied by any real number, the number does not change; that is, any number times 1 is equal to itself. The number "1" is called the multiplicative identity for real numbers.
There is a matrix which is a multiplicative identity for matrices—the
identity matrix:
I = |
= |
= |