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