Two $n \times n$ matrices $A$ and $B$ have a common eigenvalue 2 , and the same corresponding nonzero eigenvector. Which of the following options is/are correct?

(Note: $I$ is the $n \times n$ identity matrix.)

Given that $\vec{F}(x, y, z)=\sin (y) \hat{x}+\cos (x) \hat{y}+5 \hat{z}$, the integral $\iint_S \vec{F}(x, y, z) \cdot \overrightarrow{d s}$ over the unit sphere $S$ centered at the origin evaluates to $\_\_\_\_$ . (Round off to one decimal place)

A is an $m \times m$ skew-symmetric matrix with real-valued entries, and $x$ is an $m$-dimensional column vector with real-valued entries such that $x^T x=1$. The quantity $x^T A x$ evaluates to $\_\_\_\_$ . (Answer in integer)

Which one of the following statements is ALWAYS correct about a collection of $p$ column vectors, each having $n$ real-valued entries?