# Matrix manipulation for Dirac matrices

From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I \end{pmatrix}$$ Now what do we understand by this operation $\gamma^0 \gamma^{\mu \star}\gamma^0 =\gamma^{\mu T}$

Do we have to verify the above equation by doing matrix operation details? or anything short important idea can do this quickly.

• What do you mean by anything short important idea can do this quickly.? – Sklivvz Jan 5 '13 at 20:55
• I meant that If i could understand the equation $\gamma^0 \gamma^{\mu \star} \gamma^0 = \gamma^{\mu T}$ without doing the matrix multiplication elaborately. – Unlimited Dreamer Jan 5 '13 at 21:00
• Related question by OP: physics.stackexchange.com/q/48334/2451 – Qmechanic Jan 5 '13 at 21:01