Matrices are hard as heck to learn, but once you do they can be so fun to use. Especially for cryptography!

Matrices pop up everywhere in science, such as quantum mechanics and electromagnetism, so I think your tag is safe.

And, yeah, they also can be a pain. Fortunately, we make computers do all that complicated matrix stuff nowadays; however, if you want to, say, program said computer to do that stuff, you'd better have a thorough understanding of the process of getting a row reduced echelon form or determinant.