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:
This matrix, denoted
I, is a square matrix. When any
m×n
matrix is multiplied
on the left by an
m×m identity matrix, or on the right by an
n×n identity
matrix, the
m×n matrix does not change. For example,
and
.
+ 
= 
= 
= 
