8. 3 finding inverse of a matrix

Hey today we learnt to find the A^-1 of A, commonly called the inverse of A.

Definition:

 If there exists A^-1 x A= I(n) = A^-1xA,

 A^-1 is called the inverse of A

How do you find an inverse matrix:

1. Write the nX2n matrixm( matrix A on the left and Identity matrix on the right with a dotted line separating the two)

2. Reduce A to I using elementary row operations on the entire matrix set. The result will be [I: A^-1] 

    Note : if this is not possible, A is not imversible

3. Check your work 

Here are two examples 

In example one, we used the procedures and found out the inverse

 Example two does not have an inverse!!!!!

 Note how the last matrice set is not the identity, so there is no inverse for this matrix. 

 Have you learnt something?