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Mod note: OP warned about not using the homework template.

Let ##g_{ac}## be a 3-d metric.

So the trace of a metric is equal to its dimension so I get ##g_{ac}g^{ac}=3##

But I'm a tad confused with the expression : ##g^{ac}g_{ad}##=##delta^{c}_{d}##

I thought it would be ##3delta^{c}_{d}###

Because ##delta^{c}_{d}## implies that ##g^{ac}g_{ad}## is only non-zero when c=d, in which case don't you just get: ##g_{ac}g^{ac}=3##

Let ##g_{ac}## be a 3-d metric.

So the trace of a metric is equal to its dimension so I get ##g_{ac}g^{ac}=3##

But I'm a tad confused with the expression : ##g^{ac}g_{ad}##=##delta^{c}_{d}##

I thought it would be ##3delta^{c}_{d}###

Because ##delta^{c}_{d}## implies that ##g^{ac}g_{ad}## is only non-zero when c=d, in which case don't you just get: ##g_{ac}g^{ac}=3##

**Cheers in advance.**
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