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The Pauli matrices are
X
=
[
0
1
1
0
]
X = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}
X
=
[
0
1
1
0
]
,
Y
=
[
0
−
i
i
0
]
Y = \begin{bmatrix}0 & -i \\ i & 0\end{bmatrix}
Y
=
[
0
i
−
i
0
]
, and
Z
=
[
1
0
0
−
1
]
Z = \begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}
Z
=
[
1
0
0
−
1
]
. Compute the SUM of their determinants:
det
(
X
)
+
det
(
Y
)
+
det
(
Z
)
\det(X) + \det(Y) + \det(Z)
det
(
X
)
+
det
(
Y
)
+
det
(
Z
)
.
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3
0
-3
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