Under what condition will the lines m^{2}x+ny-1=0 and n^{2}x-my+2=0 be perpendicular?

Explanation

For two lines to be perpendicular, the product of their slopes must be -1. The slope of m^2x+ny-1=0 is -m^2/n, and the slope of n^2x-my+2=0 is n^2/m. Thus, (-m^2/n)(n^2/m) = -1 \implies -mn = -1 \implies mn = 1 \implies mn-1=0.

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