Lorentz Group Clarification: Boosts & g Matrix

[Silviu]

Hello! I read that for a boost, for which we have a matrix $\Lambda$ we must satisfy $\Lambda_\alpha^\mu g_{\mu \nu} \Lambda_\eta^\nu = g_{\alpha \beta}$. I am not sure I understand this. If we have a boost along the x-axis the $\Lambda_0^0$ component is $\gamma$, but $\gamma^2 \neq 1 = g_{00}$. So how do I apply that formula? Thank you

 

[PeterDonis]

I am not sure I understand this.

Write it out explicitly in matrix form. Hint: the 0-0 component of the RHS does not depend solely on the 0-0 components of the matrices on the LHS. Remember the Einstein summation convention.