  We find the R matrix for the inhomogeneous quantum groups whose homogeneous
part is $GL_q(n)$, or its restrictions to $SL_q(n)$,$U_q(n)$ and $SU_q(n)$. The
quantum Yang-Baxter equation for R holds because of the Hecke relation for the
braiding matrix of the homogeneous subgroup. A bicovariant differential
calculus on $IGL_q(n)$ is constructed, and its application to the $D=4$
Poincar\'e group $ISL_q(2,\Cb)$ is discussed.
