ClearAll["Global`*"]

(* Input Matrix *)
A = {{a, b}, {c, d}}

cp = Collect[CharacteristicPolynomial[A, x], x]
cl = CoefficientList[cp, x]

ClearAll["Global`*"]

(* Input Matrix *)
A = {{a, b}, {c, d}}

cp = Collect[CharacteristicPolynomial[A, x], x] // TraditionalForm
cl = CoefficientList[cp, x]

ClearAll["Global`*"]

(* Input Matrix *)
A = {{a, b}, {c, d}}

cp = Collect[CharacteristicPolynomial[A, x], x] //
  PolynomialForm[#, TraditionalOrder -> True] &
cl = CoefficientList[cp, x]

ClearAll["Global`*"]

(* Input Matrix *)
A = {{a, b}, {c, d}}

c0 = Collect[CharacteristicPolynomial[A, x], x]
cx = CoefficientList[c0, x] x^Range[0, Exponent[c0, x]]
cp = Replace[Reverse@cx, List[x__] :> HoldForm[Plus[x]]]
cl = CoefficientList[cp, x]