Let $X$ be a $\mathbb{Q}$-Gorenstein (isolated) singularity of dimension at least $2$ and $f:Y \to X$ be a resolution of singularities. In this case the canonical sheaf $K_X$ is not necessarily invertible, it is only reflexive.

Question.Is the pull-back $f^*K_X$ invertible? If not, can we say that $f^*K_X/\mathrm{tors}$ is invertible?