The matrix:

$A=([a_{11},a_{12}],[a_{21},a_{22}])$

is the inverse of the matrix given by:

$B=([a,b],[c,d])$

ie: $A=B^{-1}$

Find the element $a_{11}$ of A when $a=5\mathrm{.}8,b=3\mathrm{.}7,c=2$ and $d=6\mathrm{.}2.$

Give your answer to three decimal places.