This question already has an answer here:
On an exam, the question was asked wether any matrix A can be written as the sum of a matrix B and a antisymetric matrix C.
I answered yes because just take C as the zero matrix and thus A = A + 0. I believe this is correct since the definition of a antisymetric matrix
A = -AT
holds for a matrix filled with zeros. But I'm not enterely convinced if the zero matrix is not a special case that does not count.