How do you manually prove if a Vector is a Subspace or not, given the following:

1)V= IR ^(2*2) , S={(a_11= a, a_12= b, a_21= c, a_22= d) : a+d= 0,b+c=0}

2) V= IR ^(3), S= {(a, b, c) : ab = 0 }