• # question_answer The set of all $2\times 2$ matrices which commute with the matrix with respect to matrix$\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]$multiplication is A)  $\left\{ \left[ \begin{matrix} a & b \\ c & a-b \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}$ B)  $\left\{ \left[ \begin{matrix} a & b \\ b & c \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}$ C) $\left\{ \left[ \begin{matrix} a-b & b \\ b & c \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}$ D)  $\left\{ \left[ \begin{matrix} a & b \\ b & a-b \\ \end{matrix} \right];\,\,a,\,\,b\,\,\in \,R \right\}$

Let the matrix be $\omega =\frac{3v}{4l}$ $T=2\pi \,\sqrt{\frac{L}{g}}$ $\frac{L}{2}$ $\Rightarrow$ $T=2\pi \sqrt{\frac{L}{2g}}$           $\Rightarrow$ $M=(AL)d\,\,\,\Rightarrow \,\,\frac{M}{Ad}$            $\Rightarrow$ Set of all matrices that commute with $T=2\pi \,\,\sqrt{\frac{M}{2Adg}}$ w.r.t. Matrix multiplication $\Delta DBS,$