Inverse of a matrix by using determinants

Essential property: If A is invertible→ |A| ≠ 0

then, since we have A·A-1 = I

Let the cofactor matrix

Then
 
NOTE: (AdjA)t is called adjoint or adjugate.
 
Example:
 
 
Exercises:
 
1.- Calculate the inverse of these matrices:
 
 
2.- Find the values of k to make A invertible:
Calculate A-1 when k = -5
 
 
 
 
 
 
 
 
 
 
Solutions:
1)
2) k ≠ -8
 

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