1. The problem is to understand the concept of a trace in linear algebra. 2. The trace of a square matrix is defined as the sum of the elements on the main diagonal. 3. For example, if we have a matrix $$A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix},$$ then the trace is $$\text{trace}(A) = a_{11} + a_{22}.$$ 4. The trace is useful in many areas such as finding eigenvalues, invariants, and in physics for operators. 5. To compute the trace, simply add the diagonal elements of the given matrix.