Let a, $$\lambda$$, m $$\in$$ R. Consider the system of linear equations

ax + 2y = $$\lambda$$

3x $$-$$ 2y = $$\mu$$

Which of the following statements is(are) correct?

Let $$P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$$, where $$\alpha$$ $$\in$$ R. Suppose $$Q = [{q_{ij}}]$$ is a matrix such that PQ = kl, where k $$\in$$ R, k $$\ne$$ 0 and I is the identity matrix of order 3. If $${q_{23}} = - {k \over 8}$$ and $$\det (Q) = {{{k^2}} \over 2}$$, then

Let X and Y be two arbitrary, 3 $$\times$$ 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 $$\times$$ 3, non-zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric?