The inverse_matrix function allows to calculate online the inverse of a matrix.

The calculator can calculate online the **inverse of a square matrix**.
Let A and B be two square matrices, if B is the inverse of A, then A * B = I, I is the identity matrix.
The **matrix calculator** may calculate the **inverse of a matrix** whose coefficients have letters or numbers,
it is a formal matrix calculation calculator.

The calculator can **calculate the inverse of a matrix** with the results in exact form:
to calculate the inverse of matrix `(3,3,4),(1,2,0),(0,1,7)`, enter
inverse_matrix(`[[3;1;0];[3;2;1];[4;0;7]]`),
after calculation, the result is returned.

The calculator allows symbolic calculations, it is possible to use letters as well to **calculate the inverse of a matrix** like this:
`((a,3*a,4),(1,2*a,0),(0,c,a/2))`, enter
inverse_matrix(`[[a;1;0];[3a;2a;c];[4;0;a/2]]`),
after calculation, the result is returned.

inverse_matrix(matrix)

inverse_matrix(`[[3;1;0];[3;2;1];[4;0;1]]`) returns `[[2/7;-1/7;1/7];[1/7;3/7;-3/7];[-8/7;4/7;3/7]]`

See also

- Matrix calculator : matrix_calculator. The matrix calculator allows to do calculations with matrices online.
- Determinant calculator : determinant. The determinant function calculates online the determinant of vectors or the determinant of a matrix.
- Difference between two matrices : matrix_difference. The matrix calculators allows to calculate online the difference between two matrices with step calculations.
- Inverse matrix calculator : inverse_matrix. The inverse_matrix function allows to calculate online the inverse of a matrix.
- Product matrix calculator : matrix_product. This matrix calculator allows to calculate online the product of two matrix with calculation step.
- Solve system of linear equations : solve_equations. The solver of systems of linear equations allows to solve equations with several unknowns: system of equations with 2 unknowns, system of equations with 3 unknowns, system with n unknowns.
- Sum matrix calculator : matrix_sum. This matrix calculator allows to calculate online the sum of two matrix with calculation step.
- Trace of a matrix : trace. The matrix calculator calculates online the trace of a matrix. The trace of a square matrix is equal to the sum of the terms of its diagonal.
- Transpose matrix calculator : transpose_matrix. The matrix calculator allows to calculate online the transpose of a matrix.