## Tangent Space

Consider the group $O(1,1)$ of all $2\times2$ real matrices $A$ satisfying $AGA^T=G$ for $G=diag(1,-1)$. Find the Tangent Space $T_{E}O(1,1)$, E the Identity Matrix, (as a subspace of the vector space of matrices), and construct a basis in it.

Not sure how to start this, could anyone help me out? Thanks.