The eigen vectors of the matrix $$\left[ {\matrix{ 1 & 2 \cr 0 & 2 \cr } } \right]$$ are written in the form $$\left[ {\matrix{ 1 \cr a \cr } } \right]\,\,\& \,\,\left[ {\matrix{ 1 \cr b \cr } } \right].$$ What is $$a+b$$?

Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$

Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$ and $$G = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
What is the matrix $$F?$$

Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 \cr 0 & 0 & 2 & 1 \cr 0 & 0 & 3 & 1 \cr } } \right]$$ is