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Using properties of determinants, prove the following:`|[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2` |
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Answer» `L.H.S. = |[1,x,x^2],[x^2,1,x],[x,x^2,1]|` Applying `C_1->C_1-xC_3` `= |[1-x^3,x,x^2],[0,1,x],[0,x^2,1]|` Expanding by columns, `=(1-x^3)(1-x^3) -0+0` `=(1-x^3)^2 = R.H.S.` |
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