The inverse of a matrix: is a tool used for manipulating matrix equations and creating a variety of formulas that are useful. 

To begin: Think of a real number the inverse would be written as one over that number or that number raised to the negative one power.

Ex. 6 its multiplicative inverse would be written as 1/6 or 6 raised to the negative 1

When dealing with matrix we do not refer to the phrase division or symbolize that function with a slanted line. We rather just multiply the inverse by the inverse of the Matrix (remember matrix multiplication is not commutative)

When a matrix is multiplied by its inverse it equals an identity

Ex: Matrix A x Matrix D (the inverse of A) = I (identity) as well as D x A = I 

D= A-1

An identity matrix is one that is in absolute echelon from such that there are all zero except for a one in each of the pivot rows, all identity follow the square form N X N

1000

0100

0010

0001