you have to test the closure of vector addition and scalar multiplication

consider A. The invertible 3x3 matrices will not have the zero matrix since it is not invertible, so the space of 3x3 matrices will not be a vector space in its own right

consider D. Multiplying two diagonal matices will give you a diagonal matrix, adding together two diagonal matrices will give you a diagonal matrix.

The rest you can do in a similar manner, just go throught the properties of the respective subsets