Dear student,

There is no such main topics for matrix. In matrix all the subtopics are important.

Also it is little bit memorizing. Because you have to memorize the name and tyoes of matrices. For eg - diagonal matrix, identity matrix, idempotent matrix, orthogonal matrix, nilpotent matrix, etc.

Also you must know how to find the inverse and for that you must know how to find adjoint of a matrix. Then you should remember the properties of inverse and adjoint.
Because in exam questions can be easily framed by these properties and in previous years the properties was directly asked.
Apart from these your matrix multiplication should be fast because it is a time consuming. For 2 by 2 it is very easy but for 3 by 3 or 4 by 4 matrix it is not that easy because it includes calculation and techniques to solve.
Also if you are preparing for gate, then you must know how to find eigenvalue and eigen vectors and also your should know about caley Hamilton theorem.

So, all the topics inside a matrix chapter are important. So don't leave any topic and study / prepare as per the syllabus.