  We report on a study of the exchange tunneling reaction
D+HD$\rightarrow$D$_{2}$+H in a pure solid HD matrix and in a D$_{2}$ matrix
with 0.23$\%$ HD admixture at temperatures between 130$\,$mK and 1.5$\,$K. We
found that the exchange reaction rates,
$k_{exHD}\sim3\times10^{-27}$cm$^{3}$s$^{-1}$ in the pure HD matrix, and
$k_{exD_{2}}=9(4)\times10^{-28}$cm$^{-3}$ in the D$_{2}$ matrix are nearly
independent of temperature within this range. This confirms quantum tunnelling
nature of these reactions, and their ability to proceed at temperatures down to
absolute zero. Based on these observations we concluded that exchange tunneling
reaction H+H$_{2}\rightarrow$H$_{2}$+H should also proceed in a H$_{2}$ matrix
at the lowest temperatures. On contrary, the recombination of H atoms in solid
H$_{2}$ and D atoms in solid D$_{2}$ is substantially suppressed at the lowest
temperatures as a result of increasing of violation for resonance tunneling of
atoms when they approach each other.
