solve: first factorizes A using LU decomposition, then solves for xusing forward and backward substitution

inv: uses the same method to compute the inverse of A by solving for A^-1 in A·A^-1 = I where I is the identity*. The factorization step is exactly the same as above, but it takes more floating point operations to solve for A^-1 (an n×n matrix) than for x (an n-long vector).

Reference

https://stackoverflow.com/questions/31256252/why-does-numpy-linalg-solve-offer-more-precise-matrix-inversions-than-numpy-li/31257909