explain why when engineering a plasmid it is critically important that both the gene and the plasmid be cut...

Question

with the same restriction enzyme?

Answer 1

Because the ends need to be the same to stick together. Cutting them both with the same enzyme leaves complementary ends (like two jigsaw pieces) that can then be ligated together. If you use different ezxymes, the two pieces don't fit.

Answer 2

That makes them have the same sort of "ends" that will bond together properly. It's kind of like cutting a strip of paper with some of those scissors with the patterned blade. If you cut two strips with the same scissors, the strips can be fitted together, but if you cut two strips with scissors of two different patterns, they won't match.