Expert: Ahmed Salami - 9/26/2010

Question
Mr. Salami,

The question I have is:

A skew-symmetric matrix A has the property that A^t=-A. Suppose that A is a 2x2 skew-symmetric matrix. Find the general form of a 2x2 matrix skew-symmetric matrix.

I'm not sure how to do this question, I've been trying to work at it for a while now and need help.

Any tips are appreciated.

Thanks,
Francis

Answer
Hi Francis,
Let the 2x2 matrix be
[a b]
[c d]
Its transpose is the matrix
[a c]
[b d]
Now, for the transpose to be equal to the negative of the matrix, we must have
a = -a
c = -b
b = -c (same as the previous line)
d = -d
and we can see that this is only possible when a and d are equal to zero.
Therefore, the general form of a 2x2 skew-symmetric matrix would be
[0 x]
[-x 0]
where x can take any value.

Regards