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What are the significance of the different “moduli” for different tensors?

Coman’s book “Lie groups, Lie algebras and representations” starts with
$$
begin{pmatrix}
0 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
end{pmatrix}
$$
as the identity matrix.
Later, two other matrices are defined as
$$
begin{pmatrix}
1 & 0 & 0 \
0 & -1 & 0 \
0 & 0 & 1
end{pmatrix}
$$
and
$$
begin{pmatrix}
0 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & 1
end{pmatrix}
$$
respectively. These three are all in the special unitary group $SU(3)$. Each of these matrices is an element of a particular (real) form of the group.
Question: Why does the author write
$$
begin{pmatrix}
0 & 0 & 0 \
0 & -1 & 0 \
0 & 0 & 1
end{pmatrix}
$$
instead of
$$
begin{pmatrix}
0 & 0 & 0 \
0 & 1 & 0 \
0 & 0 & -1
end{pmatrix}
$$

A:

Actually, the interpretation of a matrix as an element in $U(n)$ requires some care.
First, the distinction between the identity matrix and minus the identity matrix is not as important to the interpretation of matrices as it might seem. What matters is the determinant of a matrix, and if we multiply two matrices, then the determinant of the product is the determinant of https://globaldefence.team/zombie-invasion-removal-tool-crack-download-mac-win/

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