An orthogonal matrix satisfies the equation . That is, . Just multiply with its transpose to see if you get (you should). Your result in part a) guarantees your off diagonal entries are zero, and the entry of is given by
Alternatively, you may use the other definition of orthogonal matrix: a square matrix whose columns and rows are orthogonal unit vectors. Substitute the exact values in and check that this is true for each row (you've already shown orthogonality for columns, and the vectors are, by definition, unit).