Finding values of a, b, c of a matrix Find for which values of $a, b, c$ the following matrix is orthogonal 

$$A=
  \left( {\begin{array}{ccc}
   \sqrt{\frac{1}{2}} &amp; a &amp; \frac{1}{2} \\
    \sqrt{\frac{1}{2}} &amp; b &amp; \frac{1}{2} \\
    0 &amp; c &amp; \sqrt{\frac{1}{2}}  \\
  \end{array} } \right)$$

I was thinking of doing this: Need to find $u_1 \cdot u_2 = u_1 \cdot u_3 = u_2 \cdot u_3=0$ and that $u_4 \cdot u_4= 1$ which should form the orthogonal basis vectors but then I got stuck when I found $u_1 \cdot u_3 \neq 0$. Am I right or this is not the way to do this? Please help.
hint: $A$ is orthogonal iff $A\cdot A^{T} = I$. You can work out the equations.
hint: $A$ is orthogonal iff $A\cdot A^{T} = I$. You can work out the equations.