Well, the dimension is bounded (above) by 3, so that limits the possibilities. I would want to work straight from the definition of linear independence.

Here is a "trick" that may help: each matrix can be regarded as a 4-vector, so determine the LI in $\mathbb{R}^4$ of:

{(a,b,c,d),(e,f,g,h),(i,j,k,l)}.