Write a function luDecomposition that takes an $nxn$ square matrix $A$ as an input argument

and performs Gaussian elimination. The output arguments should be$,$ in this order, a lower

triangular matrix $L,$ an upper triangular matrix $U,$ and a permutation matrix $P$ such that $PA=LU.$

If the matrix $A$ is not square, the function should return a value of $[]$ for each return argument.

Note that $"[]"$ is an empty array. You can create an empty array as follows: myVariable $=$

$[]$ ; $($You can of course use any variable name you would like.$)$ Test your function by running

the test stub called test$\_$luDecomposition.