OK, here is what I get when I run the code posted above:

i'm a little more lost than the others but understand det and matrix algebra well

however when i "ran your code" i just got allot of errors. here's what i'm seeing so far, and i'm not sure whether it is what your looking for or not...

In[1094]:= Module[{n, [Theta]3, s, [CapitalDelta][Theta], l3, l2, l1, [Theta]1, [Theta]2, f1, f2, F1, p1, J}, n = Real; p1[s, [Theta]3] = ({{[Theta]3}, {s}}); p1[n_] = ({{[Theta]3}, {s}}); [CapitalDelta][Theta] = 10*Pi/180; l2 = Rationalize@0.20; l3 = Rationalize@0.45; [Theta]1 = [Pi]; n = 0; [Theta]2 = Pi/6; [Epsilon] = 0.00001; [Theta]2max = 2 Pi; f1[p1[[Theta]3, s]] = sCos[[Theta]1] + l2Cos[[Theta]2] + l3*Cos[[Theta]3]; f2[p1[[Theta]3, s]] = sSin[[Theta]1] + l2Sin[[Theta]2] + l3*Sin[[Theta]3]; F1 = ({{f1[p1[[Theta]3, s]]}, {f2[p1[[Theta]3, s]]}}); p1[0] = ({{0}, {l2 + l3}}); J[p1[[Theta]3, s]] = ({{D[f1[p1[[Theta]3, s]], s], D[f1[p1[[Theta]3, s]], [Theta]3]}, {D[f2[p1[[Theta]3, s]], s], D[f2[p1[[Theta]3, s]], [Theta]3]}}); ddet = Det[({{D[f1[p1[[Theta]3, s]], s], D[f1[p1[[Theta]3, s]], [Theta]3]}, {D[f2[p1[[Theta]3, s]], s], D[f2[p1[[Theta]3, s]], [Theta]3]}})]; Print@ddet; M = MatrixForm[Inverse[J[p1[s, [Theta]3]]]] ]

During evaluation of In[1094]:= 0

Out[1094]//MatrixForm= \!( TagBox[ RowBox[{"(", "", GridBox[{ { RowBox[{"-", "1"}], RowBox[{"-", RowBox[{"Tan", "[", "[Theta]3$", "]"}]}]}, {"0", FractionBox[ RowBox[{"20", " ", RowBox[{"Sec", "[", "[Theta]3$", "]"}]}], "9"]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997], { Offset[0.7]}, Offset[0.27999999999999997]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}], Function[BoxForme$, MatrixForm[BoxForme$]]])

The problem is that you assigned MatrixForm to mat. In my original post there was a bracket (mat ...)//MatrixForm which avoids this. So please insert the brackets again.

Thank you David, if the apporoximations are not the problems,why the multiplication (last output) is printed in yhat way?

Hi Michael, i mean that matrix mat is printed with approximate number(-1.) and,for this, i cant use this matrix in a multiplication.

PS The approximation in the matrix mat is in the code posted by you.

Can someone help me?

Hello Irenzo,

coming directly back to your question: you can use Simplify[ddet = .....] to achieve the result without the leading 0. But there are some other topics: you called J[p1[s, [Theta]3] in the last line of your code with the arguments in reversed order to the definition. Unless this is on purpose this will lead to s and theta3 values being exchanged in this function. In general the style of your code can be changed to make the whole calculation much more compact:

f1 = s Cos[\[Theta]1] + l2 Cos[\[Theta]2] + l3 Cos[\[Theta]3];
f2 = s Sin[\[Theta]1] + l2 Sin[\[Theta]2] + l3 Sin[\[Theta]3];

(jmat = {{D[f1, s], D[f1, \[Theta]3]}, {D[f2, s], 
     D[f2, \[Theta]3]}}) // MatrixForm

ddet = Det[jmat]

Simplify[ddet /. {l3 -> 0.45, \[Theta]1 -> \[Pi]}]

(mat = Simplify[
    Inverse[jmat] /. {l3 -> 0.45, \[Theta]1 -> \[Pi]}]) // MatrixForm