Matrices

# Invertible matrix

A matrix

is **invertible** if

so that *A·B = B·A = I _{n}* . Otherwise it is called

**singular matrix**.

*B=A*^{-1} is called the **inverse of A**

* *

NOTE:

Properties:

Let

invertibles, then:

**Calculation of the inverse by Gauss-Jordan method**

Example:

** **

NOTE: if we obtain a row of zeros in the matrix on the left, A is a singular matrix

**Exercise**. Calculate the inverse of the following matrices:

Solutions:

** **

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