Which of the following is a nilpotent matrix

If $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\5&0&7\\6&2&5\end{array}} \right]$and $B = \left[ {\begin{array}{*{20}{c}}1&3&5\\0&0&2\end{array}} \right]$, then which of the following is defined

Express the following matrices as the sum of a symmetric and a skew symmetric matrix :  $\left[\begin{array}{rrr}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right]$

If $\mathrm{A}, \,\mathrm{B}$ are symmetric matrices of same order, then $\mathrm{A B}-\mathrm{B A}$ is a

Let $a =$$\mathop {Lim}\limits_{x \to 1} \,\,\frac{x}{{\ln \,x}}\; – \;\frac{1}{{x\,\ln \,x}}$ ; $b =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{{x^3} – 16x}}{{4x + {x^2}}}$ ; $c =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{\ln (1 + \sin x)}}{x}$ and $d =$$\mathop {Lim}\limits_{x \to  – 1} \,\,\frac{{{{(x + 1)}^3}}}{{3\left( {\sin (x + 1) – (x + 1)} \right)}}$ , then the matrix $\left[ {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right]$ is