Finding the inverse matrix requires the skills of dealing with matrices, in particular, the ability to calculate the determinant and transpose.

instructions

1

The inverse matrix is ​​obtained from the elements of the originalaccording to the formula: A ^ -1 = A * / detA, where A * - adjoint matrix, detA - determinant of the original matrix. The adjoint matrix - a matrix transpose amendments to the elements of the original matrix.

2

First get the determinant of the matrix, it isIt must be different from zero, as further determinant will be used as a divider. Suppose, for example, given a square matrix of the third order (consisting of three rows and three columns). As can be seen, the determinant of this matrix is ​​not zero, so there is an inverse matrix.

3

Search for add-ons to each element of the matrix A. Supplement to A [i, j] is the determinant of the submatrix obtained from the original by deleting the i-th row and j-th column, and this determinant is taken with the sign. The sign is determined by multiplying the determinant by (-1) in the degree of i + j. Thus, for example, in addition to A [2,1] is the determinant, discussed below. The sign was given as follows: (-1) ^ (2 + 1) = -1.

4

As a result, you get matrix ons now transpose it. Transposition - an operation which is symmetric about the main diagonal of the matrix, rows and columns are swapped. Thus, you find attached matrix A *.

5

Now divide each element by the determinant of the original matrix and get matrix the reverse of the original.