Invertible matrix

A matrix

is invertible if

so that A·B = B·A = In . 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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