Write a MATLAB function that receives a square matrix A as input, reduces A to row echelon form and returns the new matrix.

A matrix is in row echelon form if

all nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix), and

the leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it.