question_answer

For positive numbers x, y, z, the numerical value of the determinant \[\left| \begin{matrix}    1 & {{\log }_{x}}y & {{\log }_{x}}z  \\    {{\log }_{y}}x & 1 & {{\log }_{y}}z  \\    {{\log }_{z}}x & {{\log }_{z}}y & 1  \\ \end{matrix} \right|\]is

A) 0                                 

B)  1

C) 2                                 

D) None of these

Correct Answer: A

Solution :

We have,

[ \[\because \] all rows are identical]