The finitistic dimension of an Artin algebra with radical square zero

We investigate the inequality ${\rm Findim}\ ! \Lambda^{op} \leq {\rm dell}
! \Lambda$ between the finitistic dimension and the delooping level of an Artin algebra $\mathrm{\Lambda }$, and whether equality holds in general. We prove that equality $\mathrm{F}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{m}\text{\hspace{0.17em}⁣}{\mathrm{\Lambda }}^{op}=\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{l}\text{\hspace{0.17em}⁣}\mathrm{\Lambda }$ always holds for Artin algebras with radical square zero.