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A square matrix A, which is nonsingular (i.e) det(A) does not equal zero, then there exists an nxn matrix A^{1} which is called the inverse of A. An Inverse Matrix when multiplied by the original matrix yields the identity matrix. The inverse of a square n x n matrix A, is another n x n matrix denoted by A^{1} such that
A A^{1} = A^{1} A = I
Where I is the n x n identity matrix. That is, multiplying a matrix by its inverse produces an identity matrix. Not all square matrices have an inverse matrix. If the determinant of the matrix is zero, then it will not have an inverse, and the matrix is said to be singular. Only nonsingular matrices have inverses
The inverse of a general nxn matrix A can be found by using the following equation
Take for example a arbitury 2x2 Matrix A whose determinant (adbc) is not equal to zero
Where a,b,c,d are numbers, The inverse is
Matrices are widely used in geometry, physics and computer graphics applications. The array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules. Matrix calculations can be understood as a set of tools that involves the study of methods and procedures used for collecting, classifying, and analyzing data. In many applications it is necessary to calculate 2x2 inverse matrix where this online 2x2 inverse matrix calculator can help you to effortlessly make your calculations easy for the respective inputs
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