A is a real and non-symmetric matrix of order 3. prove that the rank of the matrix $A-A^t$ is 2. A is a real and non-symmetric matrix of order 3. prove that the rank of the matrix $A-A^t$ is 2.
We have $\rho(A)=\rho(A^t)$ where $\rho(A)$ is the rank of A.

Hint:
For any skew-symmetric (antisymmetric) real (in fact, over any field of characteristic$\;0\neq2$) matrix, we have that $\;\det A=(-1)^n\det A\;$ , so if $\;n\;$ is odd we get $\;\det A=0\;$
Further hint: in your case, the first two lines of $\;A-A^t\;$ are linearly independent provided $\;a_{12}\neq a_{21}\;$ . Generalize.
