Pseudo orthogonal group

Hi everyone,

Anybody knows how to prove, or at least knows the reference that shows,
that the special pseudo orthogonal group has exactly two connected
components?
By special pseudo orthogonal i mean, the group of all linear
transformations of determinant one which preserve a symmetric
nondegenerate bilinear form, or more explicitly the set of matrices
which preserve the matrix whith only pluses and minuses along the
diagonal.

BTW, are there general theorems, techniques, algorithms.. which are
used to establish the number of connected components for general lie
groups?

Thanks!
Tim

.