Front/back linocut? Is this possible?

So I need two bat wings opposite of each other - I cut out this wing shape from linoleum, and I’m wondering if I can carve the front AND back on the same slab of linoleum to get the two wings I need. So I’ll carve the one side, and flip it over and carve the other. Will this work? I only had one slab of linoleum this size, so I’m trying to make it work. I’m new to this thanks for the help!