Any good Graduate Level linear algebra textbook for practice/problem solving?
In Berkeley Problems in Mathematics book, there are a lot of problems with solutions of Linear Algebra as well as Analysis and Algebra. The problems are taken from Preliminary Exams of UC Berkeley.
There's a book by Jonathan Golan called The Linear Algebra a Beginning Graduate Student Ought to Know. I would take look at that. It has tons of pretty good problems.
I would like to recommend "Linear algebra: challenging problems for students" by Fuzhen Zhang
In addition to the Halmos book already mentioned, which is indeed excellent, there are several other problem books/solution manuals for theoretical linear algebra:
Shakarchi's Solution Manual to Lang's Linear Algebra
Blythe's Algebra Through Practice: Matrices and Vector Spaces and Algebra Through Practice: Linear Algebra
Don't overlook Schaum's outline of linear algebra. There are some good problems in there as well
Also, I would find it somewhat surprising if you couldn't find solutions to many of Axler's problems on-line.
Added:
One very good sources of problems/solutions that I neglected to mention is UC Denver's archive of past Applied Linear Algebra qualifying exams (with solutions) found here: Qualifying Exams. Don't be misled by the adjective "applied"; these problems are theoretical in nature and a similar to those found in Axler (though perhaps a little more demanding, but not by much)
the Halmos book and Blythe's book are good reference but it is elementary book in linear algebra.I suggest you Linear Algebra by Stephen H. Friedberg or Problems and Theorems in Linear Algebra by V. V. Prasolov