Find the total number of ways a 3×n3×n board can be painted using 33 colors while making sure no cells of the same row or the same column have entirely the same color. The answer must be computed modulo 109+7109+7.

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c