## Calculate the Inverse of a Matrix II

# Inverse of a Matrix theory

Inverse of a Matrix

**Definition method.**

If the product between two matrices is the identity matrix, then we say that the matrices are “inverse”; because by multiplying them we obtain the neutral element for the product .

Consider the inverse matrix:

It must accomplish that: A · A^{-1 }= I

Observe the following example.

So, we obtain the following equations system to get the inverse matrix values.

**Determinant method.**

By applying this method we say that:

Where att (A)^{t} is attached matrix and det (A) is the determinant of the matrix A.

The A determinant solution can be seen in the corresponding section about determinants theory.

att (A)^{t} is obtained as follows:

Given matrix A:

Its attached is formed by the determinings which are result by suppressing a row and column of each of one of the elements.

For example, the a_{32} element position would be occupied by the determining which results by eliminating the third row and second column, that is:

and as the row + column (3+2) is odd we change the sign.

Then we perform its transpose:

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