Quick question, index notation, alternating tensor.

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Q) I am using index notation to show that ε^{0123}=-1 given that ε_{0123}=1.

The soluton is:

ε^{0123}=g^{00}g^{11}g^{22}g^{33}ε_{0123}=-ε_{0123}

where g_{\alpha\beta} is the metric tensor.

I am struggling to understand the last equality.

Many thanks for any assistance.
 
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g00=-1, correct? Really, η00=-1.
 
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