Matrix inverse calculator is a simple linear algebra tool that calculates the inverse of a square matrix. It works for matrix of sizes 2x2, 3x3, 4x4 and 5x5.

We are working on adding support for matrices with huge sizes

The inverse of a matrix is a matrix which when multiplied with its original matrix results in identity matrix.

Identity matrix meaning, a matrix with 1's in the diagonal and 0 elsewhere

To calculate the inverse matrix, we must at first make sure the matris is a square matrix.

After that, we have to calculate the determinant of the matrix.

Then we have to calculate the adjoint of the matrix.

Finally, we calculate the inverse matrix using the formula: inverse = adjoint / determinant, where each element of adjoint matrix is divided by the determinant of the matrix.

Inverse of matrices can be used to solve linear equations.

During the initial phase of learning about matrices, students often get confused between the transpose and inverse of a matrix.

But transpose adn inverse of matrices are completely different concepts.

Transpose is merely changing rows and columns

But calculating inverse involves a lot of calculations

And calculating the transpose of a matrix as the size of matrix increases does not increases much complexity.But calculating the inverse of a matrix as the size of matrix increases increases the complexity exponentially

Take a 2 by 2 matrix B = [ [2,3] [4,5] ]

The inverse of matrix B is [ [-5/2, 3/2] [2, -1] ]

You can verify if the matrix is a inverse by multiplying it with original matrix, you should get identity matrix

Take a 3 by 3 matrix B = [ [1,2,3] [0,1,4] [5,6,0] ]

The inverse of matrix B is [ [-24, 18, 5] [20, -15, -4] [-5, 4, 1] ]

To verify, you can use the inverse matrix calculator above to check if the matrix is correct or not