How to find the inverse of a 2x2 matrix using gaussian elimination (not using rref or lu)?

Thanks

Answer 1

[Jim Riggs]

The inverse of a 2x2 is very easy to calculate:

In terms of Matlab code:

detA = A(1,1)*A(2,2)-A(1,2)*A(2,1);
Ainv = (1/detA)*[A(2,2),-A(1,2);-A(2,1),A(1,1)];

(note that if detA is zero, the matrix has no inverse)

[John Staine]

And how would i code it so it uses Gaussian elimination process to find the inverse?

[Jim Riggs]

Gaussian elimination is not needed unless the matrix rank is greater than 3. For rank 2 and 3 there is a closed-form solution which is more efficient.

Answer 2

[the cyclist]

I found this answer by googling.