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I have this question on my assignment that's confusing me, I think I have the logic right, but for some reason Im getting the wrong answer..

Anyways the question states:

If S is the subspace of M5 (R) consisting of all matrices with trace 0, then dim(S) = ?

Now, I know the trace is the sum of entries in the main diagonal, so I assumed that all the elements on the diagonal are zero..

Which leaves me with 28 non-zero elements above the diagonal and 28 below, which gives a total of 56 elements.. hence a dimension of 56?

However that was wrong.. now I know that for a skew symmetrix matrix of 8x8 we'd have a dimesion of 28 since the ones above are the negative of the ones below.. can anyone please help me out?

I had 6 tries for the question.. and I only have one left!! Any help would be greatly appreciated.. I tried 28, 56, and 60, all were wrong..

Thank you very much!

AZH