Unlike scalars, division by a matrix or vector is not defined.  The inverse  of a matrix is a sort of equivalent division by a matrix. Inverse are usually associated with square matrix. A special type of square matrix is the identity matrix.

All elements except the principal diagonal are zero
The elements on the principal diagonal are 1's
The determinant |I| = 1
A I = I A = A

In MATLAB you can generate the identity matrix
» eye(4)       % generate I _4x4
ans =
      1            0            0            0
      0            1            0            0
      0            0            1            0
      0            0            0            1