Let A be the 2 ×2 matrix given by A=(a_ij) where aij $\in${0,1,2,3,4} such that a₁₁ + a₁₂ + a₂₁ + a₂₂ = 4
then which of the following statement(s) is /are true?

$\text{ a) }\left(\begin{array}{l}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\end{array}\right),\left(\begin{array}{l}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\end{array}\right),\left(\begin{array}{l}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\end{array}\right)\left(\begin{array}{l}4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right),\left(\begin{array}{l}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}4\end{array}\right)$

b) using 0,0,2,2$\to$ there are two matrices which are invertible $\left(\begin{array}{l}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\end{array}\right),\left(\begin{array}{l}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\\ 2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\end{array}\right)$

using 0,0,1,3$\to$ there are four matrices which are invertible

using 0,1,1,2$\to$there are twelve matrices which are invertible

using 0,0,0,4 and using 1,1,1,1 no matrix is formed,
which is invertible $\therefore$total 18

$\text{ c) }|4-(-4\left)\right|=8$

d) there are five matrices, which are either symmetric or skew symmetric and whose determinant is divisible by 2