Which of the following is an orthogonal matrix ?

Options

A. `[(6//7,2//7,-3//7),(2//7,3//7,6//7),(3//7,-6//7,2//7)]`
B. `[(6//7,2//7,3//7),(2//7,-3//7,6//7),(3//7,6//7,-2//7)]`
C. `[(-6//7,-2//7,-3//7),(2//7,3//7,6//7),(-3//7,6//7,2//7)]`
D. `[(6//7,-2//7,3//7),(2//7,2//7,-3//7),(-6//7,2//7,3//7)]`

Answer

A

Explanation

Matrix `[(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))]` is orthogonal if
`sum a_(i)^(2)=sum b_(i)^(2)=sun c_(i)^(2)=1, sum a_(i)b_(i)=sum b_(i)b_(i)=sum c_(i)a_(i)=0`