In a two-dimensional stress analysis, the state of stress at a point P is\(\left[ \sigma \right] = \left[ {\begin{array}{*{20}{c}} {{\sigma _{xx}}}&{{\tau _{xy}}}\\ {{\tau _{xy}}}&{{\sigma _{yy}}} \end{array}} \right]\)The necessary and sufficient condition for existence of the state of pure shear the point P, is

• A. \({\sigma _{xx}}{\sigma _{yy}} - \tau _{xy}^2 = 0\)
• B. Τxy = 0
• C. σxx + σyy = 0
• D. \({\left( {{\sigma _{xx}} - {\sigma _{yy}}} \right)^2} + 4\tau _{xy}^2 = 0\)