yes, it is both symmetric as well as skew symmetric
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In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
I could be wrong but I do not believe that it is possible other than for the null matrix.
My knowledge limits to square matrices. The answer is yes, because 0 = -0
In a skew symmetric matrix of nxn we have n(n-1)/2 arbitrary elements. Number of arbitrary element is equal to the dimension. For proof, use the standard basis.Thus, the answer is 3x2/2=3 .
No, there cannot be any.