Can MATX physically fits into ATX casing?

Unless your computer is an office computer or a gaming computer (neither seems likely) then the case should work with just about any motherboard except a motherboard that's meant for gaming. The brand name of the motherboard should be printed on the front (not back) of the board. It's located on various spots on the motherboard depending on manufacturer and model so it would be difficult to tell you a way to identify it if it's not printed on the computer's case. You could try looking at the manufacturers website and find your computers information on there.