Definition:
Identity Matrix  The identity matrix I for multiplication is a square matrix with a 1 for every element of the principal diagonal (top left to bottom right) and a 0 in all other positions. 
Back in multiplication, you know that 1 is the identity element for multiplication. Whenever the identity element for an operation is the answer to a problem, then the two items operated on to get that answer are inverses of each other.
This is also true in matrices. If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
Definition:
Inverse Matrix  The matrix which when multiplied by the original matrix gives the identity matrix as the solution. 
Likewise we will (in the next lesson) use an inverse matrix to multiply both sides of a matrix equation to solve the equation.
To find an inverse matrix:


Given Problem. 

First check if the determinant is zero. If it is not zero, then the inverse we are trying to find exists. 

Now use the inverse formula to find and calculate the inverse matrix. 

Check. 