This document discusses inverse matrices and methods for calculating them. It defines an inverse matrix as a matrix M-1 such that MM-1=M-1M=I, where I is the identity matrix. Only square matrices can have inverses. Two common methods for calculating the inverse are Crammer's Method, which uses the adjoint and determinant of the matrix, and Gauss Method, which performs row operations. An example calculates the inverse of a 2x2 matrix using the property that the inverse is the transpose of the cofactor matrix divided by the determinant.

2. SUBMITTED BY:
Syed Ahmed Zaki
ID No: 131-15-2169
Section: A
Dept. of Computer Science and Engineering
1st year,2nd Semester
Summer 2013
Submission Date : 19 August 2013

3. SUBMITTED TO:
Mohammad Salek Parvez
Assistant Professor
Department of Natural Science
Faculty of Science and Information Technology
Daffodil International University

4. INVERSE MATRIX
As usual the notion of inverse matrix has been developed in
the context of matrix multiplication.Every nonzero number
possesses an inverse with respect to the operation ‘number
multiplication’
Definition: Let ‘M’ be any square matrix.An inverse matrix of
‘M’ is denoted by ‘푀−1’ and is such a matrix that 푀푀−1=
푀−1푀=퐼푛
Matrix ‘M’ is said to be invertible if 푀−1 푒푥푖푠푡푠. Non-square
matrices do not have inverses.
Note: Not all square matrices have inverses. A square matrix
which has an inverse is called invertible or nonsingular, and a
square matrix without an inverse is called noninvertible or

5. EXAMPLE
Example:
M=
4 3
3 2
and It’s inverse is 푀−1 =
−2 3
3 −4
since
푀푀−1=
4 3
3 2
−2 3
3 −4
=
1 0
0 1
푀−1푀=
−2 3
3 −4
4 3
3 2
=
1 0
0 1
Therefore,
4 3
3 2
and
−2 3
3 −4
are inverses of each other

6. METHOD
There are usually two methods to find the
inverse of a matrix. These are:
(a) Crammer’s Method
(b) Gauss Method

7. CRAMMER’S METHOD
Equation:
푀−1 =
1
푀
(adj M)
Flowchart :
•Matrix M
• Cofactor M[Cof (M) ]
• Adjoint M[adj (M) ]
• Inverse Matrix:푀−1

8. EXAMPLE

9. GAUSS METHOD FOR INVERSION

10. SHORTCUT METHOD

11. THE END