Computing an Inverse of a Matrix

A square matrix that is not invertible is called singular or degenerate.
A square matrix is singular if and only if its determinant is 0.

The easiest way to compute the inverse of a matrix is using the formula of RREF, where you augment the matrix with it’s identity and the resulting RREF’s augmented matrix is the Matrix Inverse:

rref[A|I] –> [I|A¯¹]

Another way to compute the inverse of a matrix is by:

1. Compute the determinant.
2. Computing the adjugate matrix which is the hadamard multiplication of minor determinant matrix with the cofactors(plus/minus) matrix.
3. Lastly, dividing each element by the determinant, calculated in clause 1.