Let $w>0$.compute the matrix $e^{A}$.

Question

Let $w>0$.compute the matrix $e^{A}$,where $$A=\begin{bmatrix} 0 & w \\ -w& 0 \\ \end{bmatrix}$$

Answer 1

let $A=wX$, where $X=\pmatrix{0&1\cr-1&0\cr}$ and $w>0$.Now on expanding we will get $e^{A}$=$I(\cos w)+X(\sin w)$ which will ultimately give $$e^{A}=\begin{bmatrix} \cos w & \sin w \\ -\sin w& \cos w \\ \end{bmatrix}$$