Inverse Matrix Calculator

How does this inverse matrix calculator work?

This inverse matrix calculator can help you when trying to find the inverse of a matrix that is mandatory to be square. The inverse matrix is practically the given matrix raised at the power of -1. The inverse matrix multiplied by the original one yields the identity matrix (I). In other words:

M * M^-1 = I

Where:

M = initial matrix

M^-1 = inverse matrix

I = identity matrix which is the matrix equivalent to 1.

Please take account of the fact that not all the square matrices have inverses, thus those having an inverse are called nonsingular or invertible, while square matrices that do not have an inverse are considered singular or noninvertible. A square matrix has an inverse only if its determinant is different than zero (det(M) ≠0). In case its determinant is zero the matrix is considered to be singular, thus it has no inverse.

1. Formula for finding the inverse of a 2x2 matrix.

2. Formula for finding the inverse of a 3x3 matrix requires to find its determinant, cofactor and finally the adjoint matrix and the apply one of the following formulas:

Where: adjoint represents the matrix that results by taking the transpose of the cofactor matrix of a given matrix, usually written as adj(A).

Please note that the above formulas are applicable for any n x n square matrices where the determinant is different than zero.

3. Formula for finding the inverse of a 4x4 matrix is similar to the one of a 3x3 matrix.

Please note that this calculator supports both positive and negative numbers, with or without decimals and even fractions. Fractions should be input within the form by using the "/" sign: for example input 1/5 or -1/2.