Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\,\,{\left[ D \right]_{5x3,}}$$ $$\,\,{\left[ E \right]_{5x5,}}$$ $$\,\,{\left[ F \right]_{5x1,}}$$ are given. Matrices $$\left[ B \right]$$ and $$\left[ E \right]$$ are symmetric. Following statements are made with respect to their matrices.
$$(I)$$ Matrix product $$\,\,{\left[ F \right]^T}\,\,$$ $$\,\,{\left[ C \right]^T}\,\,$$ $$\,\,\left[ B \right]\,\,$$ $$\,\,\left[ C \right]\,\,$$ $$\,\,\left[ F \right]\,\,$$ is a scalar.
$$(II)$$ Matrix product $$\,\,{\left[ D \right]^T}\,\,$$ $$\,\left[ F \right]\,\,$$ $$\,\left[ D \right]\,\,$$ is always symmetric.
With reference to above statements which of the following applies?

The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are

Given matrix $$\left[ A \right] = \left[ {\matrix{ 4 & 2 & 1 & 3 \cr 6 & 3 & 4 & 7 \cr 2 & 1 & 0 & 1 \cr } } \right],$$ the rank of the matrix is

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$