For each part, find a specific example of a matrix satisfying the given properties. You must show that your example satisfies the described properties?

(c) A 3 x 3 matrix A3 such that for every permutation matrix P (Note. There are 6 of them), there exists a lower triangular matrix L and an upper triangular matrix U such that PA3 = LU. (d) A singular matrix A. such that there exists a lower triangular matrix L and a unit upper triangular matrix U such that A4 = LU