Identify the correct statement.

A. If system of n simultaneous linear equations have a unique solution, then coefficient matrix must be non-singular.$\Rightarrow$Option A is incorrect

B. If system of n simultaneous linear equations has a unique solution, then coefficient matrix must be non-singular$\Rightarrow$Option B is correct

C. since, $A^{-1}=\frac{adj.\text{A}}{\left|\text{A}\right|}\left({\text{suppose\hspace{0.17em}A}}_{n\times n}\right)\&\left|A^{-1}\right|=\left|\frac{adj.A}{\left|A\right|}\right|=\frac{{\left|A\right|}^{n-1}}{{\left|A\right|}^n}=\frac{1}{\left|A\right|}$ 

If $A^{-1}$ exists, then $adj.A$ is a non-singular matrix$\Rightarrow {(adj.A)}^{-1}$must exist$\Rightarrow$Option C is incorrect

D. We have $F\left(x\right)F\left(y\right)=\left[\begin{array}{ccc}\cos x& -\sin x& 0\\ \sin x& \cos x& 0\\ 0& 0& 0\end{array}\right]\left[\begin{array}{ccc}\cos y& -\sin y& 0\\ \sin y& \cos y& 0\\ 0& 0& 0\end{array}\right]=\left[\begin{array}{ccc}\cos (x+y)& -\sin (x+y)& 0\\ \sin (x+y)& \cos (x+y)& 0\\ 0& 0& 0\end{array}\right]=F(x+y)$