IA = A
The matrix I is called an identity matrix because IA = A and AI = A for all matrices A. This is similar to the number 1, which is called the multiplicative identity, because 1a = a and a1 = a for all real numbers a.
There is no matrix that works as an identity for matrices of all dimensions. For N×N square matrices there is a matrix IN×N that works as an identity.
If IN×N is the N-dimensional identity matrix, then its elements are 1 on the main diagonal and 0 elsewhere.
1 0 0 0 1 0 0 0 1
The main diagonal consists of those elements [I]m m where the row number is equal to the column number. At left is an example of an identity matrix.
The 1s must run down that particular diagonal; it won't work with the other diagonal.