What is inverse of a matrix ?
For a square matrix A, the inverse is written A^{1}. When A is multiplied by A^{1} the result is the identity matrix I. 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 non invertiable or singular.
Formula to find the inverse of the matrix :
Example 1 :
Find the inverse of the following matrix

Solution :
A = 2(2+1)  1(21) + 1(11)
A = 2(3)  1(1) + 1(2)
A = 612
A = 3 ≠ 0
Since A is a non singular matrix. A^{1} exists.
Example 2 :
Find the inverse of the following matrix

Solution :
A = 1(22)2(42)+1(2+1)
= 1(0)  2(6)+1(3)
= 12 + 3
A = 15 ≠ 0
Since A is a non singular matrix. A^{1} exists.
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