# Finding the inverse metric tensor from a given line element

Defining dS2 as gijdxidxj and
given dS2 = (dx1)2 + (dx2)2 + 4(dx1)(dx2). Find gij

Now here is my take on the solution: Since the cross terms are present in the line element equation, we can say that it's a non-orthogonal system. So what I did was express the metric tensor in form of a 2x2 matrix, and checked the corresponding coefficient in the equation. But I am having a problem getting to the cross terms, and how to find the corresponding coefficients to the metric tensor.

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phyzguy
Isn't $g^{ij}$ just the inverse of the 2x2 matrix representing $g_{ij}$?

vela
Staff Emeritus