Let $A= \left\lbrack \begin{array}{cc} 3 e^{3 t} & 2 e^{4 t} \\ 6 e^{3 t} & 3 e^{4 t} \end{array} \right\rbrack$.

(a) Find the determinant of $A$.
$\det (A) =$ ,

(b) Find the matrix of cofactors of $A$.

$C =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(c) Find the adjoint of $A$.
${\rm adj}(A) =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(d) Find the inverse of $A$.
$A^{-1} =$
 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$