Generalized Hooke's Law in Stiffness form derivation?

I need to derive the matrix form of the stiffness for the generalized Hooke's Law starting from:

[epsilon]=1/E[C][sigma] for the normal stresses only (Isotropic material)

Basically, I need to end up with the same equation but with [sigma] on the LHS. So, starting from strain on LHS and ending up with stress on LHS.

I thought I would get it through inverting the compliance matrix, but I don't seem to be able to.

Can someone show me how it's done.

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