If the matrix $A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}$ is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?

If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \ldots$

If $A = \begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}$, $B^{-1} = \begin{bmatrix} \dfrac{1}{5} & \dfrac{2}{5} \\ \dfrac{2}{5} & -\dfrac{1}{5} \end{bmatrix}$, then $(AB)^{-1} = $

If $A = [a_{ij}]_{3 \times 3}$ is a matrix such that $a_{ij} = |2i - 5j|$, where $|.|$ denotes the modulus function, then the element in the $2^{\text{nd}}$ row and $3^{\text{rd}}$ column of $A^{-1}$ is ...