Inverse of Matrix :
After calculating determinant, adjoint from the matrix as in the previous tutorials a) Find determinant of A (|A|)
b) Find adjoint of A (adj A)

we will be calculating the inverse using determinant and adjoint
c) Calculate the inverse using the formulae
      A^-1 = adjoint A / |A|
An Example:
For an example we will find the inverse for the following matrix

Matrix A

1 3 1 1 1 2 2 3 4

a)Finding determinant of A:
        |A| = 1x(1x4-3x2) + 3x(1x4-2x2) + 1x(1x3-2x1)
        |A| = 1x(4-6) + 3x(4-4) + 1x(3-2) = -2+0+1
        |A| = -1

b)Finding Minors of A:
        M₁₁ = 1x4-3x2 = 4-6 = -2
        M₁₂ = 1x4-2x2 = 4-4 = 0
        M₁₃ = 1x3-2x1 = 3-2 = 1
        M₂₁ = 3x4-3x1 = 12-3 = 9
        M₂₂ = 1x4-2x1 = 4-2 = 2
        M₂₃ = 1x3-2x3 = 3-6 = -3
        M₃₁ = 3x2-1x1 = 6-1 = 5
        M₃₂ = 1x2-1x1 = 2-1 = 1
        M₃₃ = 1x1-1x3 = 1-3 = -2

c)Forming Minors Matrix of A:

Matrix of minors

-2 0 1 9 2 -3 5 1 -2

d)Forming Cofactor Matrix of A:

Matrix of cofactors
-2 x 1 0 x -1 1 x 1 9 x -1 2 x 1 -3 x -1 5 x 1 1 x -1 -2 x 1	=	-2 0 1 -9 2 3 5 -1 -2

e)Forming Adjoint A:

Adjoint Matrix (Adj A)

-2 -9 5 0 2 -1 1 3 -2

f) Finding the Inverse Matrix of A

Inverse of Matrix (A-1)
A-1 = ajd A / |A| =	1/-1	-2 -9 5 0 2 -1 1 3 -2

A-1

=

2 9 -5 0 -2 1 -1 -3 2