For part 1 merely apply the principle given to the matrix. is, by the principle, the first column of your matrix. This column is all zeros. Similarly, the first column is , etc.
For part 2, apply part 1. , and we know what is. Part 3 immediately follows.
For part 4, note that is the column of . For example, we wish to show that all the columns of are zero but (just adding a formula to part 2 - ) and we are done as and is the zero vector.