The failure mode I've seen with ChatGPT in technical things is it's right often enough that when it's wrong it's hard for you to catch unless you know more than it does. I guess that's true of teachers sometimes as well, but it's easier to rely habitually on ChatGPT's judgment.
For linear algebra specifically, the software tools like Matlab, Octave, Sage, and R are so good that they can answer a lot of your questions. You can even ask ChatGPT e.g. "3x3 matrix A having columns (4,2,2), (-1,1,-1), and (6,6,8) and an eigenvalue of 2, print a GNU octave command to find the eigenvalues and eigenvectors of A."
For linear algebra specifically, the software tools like Matlab, Octave, Sage, and R are so good that they can answer a lot of your questions. You can even ask ChatGPT e.g. "3x3 matrix A having columns (4,2,2), (-1,1,-1), and (6,6,8) and an eigenvalue of 2, print a GNU octave command to find the eigenvalues and eigenvectors of A."