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Learn, or revise, determinants, matrix inverses, Gaussian elimination and eigenvalues/eigenvectors.
Determinant of 2 by 2 and 3 by 3 matrices (a Further Maths topic). Cramer's Rule (a First Year university topic).
Inverse of 2 by 2 and 3 by 3 matrices (a Further Maths topic).
Solving systems of equations using Gaussian elimination and LU factorisation; matrix inversion using Gauss-Jordan elimination. A First Year university topic.
Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors of square matrices. You may possible have met this if you've done Further Maths or the equivalent.