An important part of solving a linear system efficiently is to avoid explicitly calculating the inverse, if possible. In MATLAB, this is often done using the mldivide (\) operator. See the page here for a high-level description of the various methods/optimizations it uses.
So in a function, something like:
inv(T)*inv(A)*x
can be replaced with:
T\(A\x)
On a related note, the transpose of a matrix or array x is written as x' in MATLAB.
