This is a textbook on matrices and linear algebra course. It is written according to B.A./B.Sc.- Maths unified syllabus of Uttar Pradesh. It also covers the following topics: Matrix Algebra, Determinants, Cramer's Rule, Rank of a matrix, Gauss Elimination Method, System of Linear Equations, Eigenvalues and Eigenvectors, Cayley Hamilton's theorem, Vector Spaces, Subspaces, base, dimensions, Linear Transformations, Matrix representations, Inner product spaces and Bilinear forms.