Why there is a minus sign before $p^0$?

In scattering amplitudes, page 244, I am trying to verify that $$
p_{adot{b}} = left( begin{matrix} -p_0+p_3 & p_1-ip_2 p_1+ip_2 & -p_0-p_3 end{matrix} right), quad (1)
$$ i.e, equation (A.11).

By definition (A.1), (A.2), (A.10):
begin{align}
& sigma^{mu}=(1, sigma^i)_{adot{b}}, bar{sigma}^{mu}=(1, -sigma^i)^{dot{a}b},
& sigma^1=left( begin{matrix} 0 & 1 1 & 0 end{matrix} right), sigma^2=left( begin{matrix} 0 & -i i & 0 end{matrix} right), sigma^3=left( begin{matrix} 1 & 0 0 & -1 end{matrix} right),
& p_{adot{b}} = p_{mu} (sigma^mu)_{adot{b}}, p^{dot{a}b} = p_{mu}(bar{sigma}^{mu})^{dot{a}b}.
end{align}

We have
begin{align}
p_{adot{b}} & = p_mu (sigma^mu)_{adot{b}} = p_0 left( begin{matrix} 1 & 0 0 & 1 end{matrix} right) + p_1 left( begin{matrix} 0 & 1 1 & 0 end{matrix} right) + p_2 left( begin{matrix} 0 & -i i & 0 end{matrix} right) + p_3 left( begin{matrix} 1 & 0 0 & -1 end{matrix} right)
& =left( begin{matrix} p_0+p_3 & p_1-ip_2 p_1+ip_2 & p_0-p_3 end{matrix} right). quad (2)
end{align}
The result (2) I got has positive sign before $p^0$. Am I missing something? Thank you very much.