I have derived the formula for inversing a $2\times 2$ matrix.
You can access the pages where i have derived the formula for inverse of $2\times 2$ matrix :
Those who don't want to mess with the page links above can use the below linked video : I used this video as a guide to derive the formula for inverse of $2\times 2$ matrix - Determining the Inverse of a Matrix Algebraically
The formula goes like this : $$A^{-1} = \dfrac{1}{\det(A)}\cdot\operatorname{adj} (A)$$
As i try to derive the formula for inversing a $3\times 3$ matrix, it became exponentially difficult. Can anyone please guide me with the derivation?
Thanks a lot! Hope this will help many who love Matrices :)
Just find the cofactor matrix, then the adjunct matrix is the transpose of that. Divide the adjunct by the determinant of the original matrix, e.g.
$$A^{-1}=\frac{1}{\det A}C^\text{T},$$
where $C$ is the cofactor matrix and $\det A\neq 0$.
Since you are a developer, and if you're trying to implement this, you may want to use an existing matrix library as many of them will be optimized for efficiency, e.g. using LU decomposition.
Ps tried clicking your page links but then it asks for my email account!
You can always find the general inverse of any square matrix by augmenting it with the identity matrix, then use Gaussian elimination (putting it into reduced row echelon form), so that you get the identity on the left. Whats on the right will be the inverse.
You may find this link useful.