let M_n(c) denote the n times n matrices over the complex number field. N be a subspace of

M_n(C).

1. if all the matrices in N are non-invertible , what is the maximum of the dimension of N can be?

2. if all the matrices in N commute with each other , what is the maximum of the dimension of N can be?

3. if all the matrices in N are nilpotent , what is the maximum of the dimension of N can be?

4. if all the non-zero matrices in N are invertible , what is the maximum of the dimension of N can be?