Which of the following is/are not true ?
I) If 1 is not a prime number, then 2 is not a prime number.
II) e is a vowel and $12 \times 3 = 36$
III) It is not true that 14 is a composite number and 3 is even number.
IV) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.

The negation of the inverse of the statement $\sim p \vee \sim q$ is...

If $A = \begin{bmatrix} 3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5 \end{bmatrix}$, $B = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}$ such that $XA = B^T$ and $A^{-1}Y = B$, then $XY = $

Let $A = \begin{bmatrix} a & 1 \\ 1 & b \end{bmatrix}$, where $a$ and $b$ are the roots of the equation $x^2 - 4x + 2 = 0$. If $A + A^{-1} = kI_2$, then the value of $k$ is ____