coerce matrix into unitary groups

Question

I try to coerce this matrix

\begin{pmatrix} -1 & 0\\ 0 & 1\\ \end{pmatrix}

into $GU(2,9)$. I used the following command:

K:=FiniteField(9);

G:=GeneralUnitaryGroup(2,K);

G![[K.1^4,0],[0,1]];

Why I keep getting error message telling me:

Runtime error in '!': Element is not in the group

LHS: GrpMat

RHS: [[]]

At last, I checked the first generator of GU(4,9) from Magma:

[  K.1     0     0     0]
[    0     1     0     0]
[    0     0     1     0]
[    0     0     0 K.1^5]

So this matrix doesn't satisfy "transpose multiplied by conjugate equals I".. So how the GU is defined here?

Answer 1

This might do what you want:

K:=FiniteField(9);
G:=GeneralUnitaryGroup(2,K);
tmat :=TransformForm(IdentityMatrix(GF(9),2), "unitary");
GG := G^(tmat^-1);
GG![[K.1^4,0],[0,1]];