The short answer is 'no.' You should not clean any cookware or bakeware with steel wool or other other harsh cleaning tools.
While cleaning stainless steel cookware with steel wool won't noticeably reduce the cookware's performance, it will likely scratch the surface and reduce longevity.
Never use steel wool to clean cookware with a coated surface—like nonstick or ceramic—as it will damage the coating and significantly reduce its effectiveness.
Always refer to the use & care guidelines that came with your cookware before cleaning it.
