  Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a
field $K$ and $I$ be a monomial ideal of degree $d\leq 2$. We show that
$(I^{k+1}:I)=I^k$ for all $k\geq 1$ and we disprove a motivation question that
was appeared in \cite[Question 2.51]{CHHV} by providing of a counterexample.
Also, by this counterexample, we give a negative answer to the question that
depth function of square-free monomial ideals are non-increasing.
