Assess students' ability to solve systems of linear equations using Gaussian elimination (row operations on augmented matrices) and by computing matrix inverses when applicable. Include 2x2 and 3x3 examples requiring row-reduction to echelon or reduced echelon form, identification of invertibility (via determinants or row operations), solving Ax = b using A^{-1}, and interpreting consistency (unique solution, infinite solutions, or no solution). Expect procedural execution, clear justification of steps, and interpretation of results.