Product of two involutions in quaternionic special linear group

An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as a product of two involutions. In this paper, we classify the reversible and strongly reversible elements in the quaternionic special linear group $\mathrm{S}\mathrm{L}(n,\mathbb{H})$ and quaternionic projective linear group $\mathrm{P}\mathrm{S}\mathrm{L}(n,\mathbb{H})$. We prove that an element of $\mathrm{S}\mathrm{L}(n,\mathbb{H})$ (resp. $\mathrm{P}\mathrm{S}\mathrm{L}(n,\mathbb{H})$) is reversible if and only if it is a product of two skew-involutions (resp. involutions).