Linear Algebra has occupied a very crucial place in Mathematics. Linear Algebra is a continuation of classical courses in the light of the modern development in Science and Mathematics, We must emphasize that mathematics is not a spectator sport, and that in order to understand and appreciate mathematics it is necessary to do great deal of personal cogitation and problem solving. Throughout the book the author follows the practice of first presenting required background material, which is then used to develop the results. Relevant material is included in each chapter from other sources improves readability and makes the presentation "self-contained" to a large extent. In addition, at the end of each chapter a comprehensive Exercise is provided so that the interested reader can explore in more depth. All the examples have been completely solved. The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The students should first try to understand the theorems and then they should try to solve the questions independently. Each topics included in the book is important for degree students of Indian universities.