Linear Algebra Basics

with(LinearAlgebra):
A := Matrix([[1, 2], [3, 4]]);
Determinant(A);
MatrixInverse(A);

with(LinearAlgebra) loads the package once at the top of a session -- after that, Matrix, Determinant, MatrixInverse and similar commands are available directly.

Solving a linear system

b := Vector([5, 6]);
LinearSolve(A, b);

Why This Matters for Your Exams

Determinant and inverse computations get error-prone fast by hand past 2x2 -- use Maple to check a hand-worked answer, not to skip learning the method itself.