JEE Main 202226 Jun, Evening shiftMathematicsHardMatrices and Determinants245× since 2002Let X=[010001000], Y=αI+βX+γX2X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & 0 & 0 \cr } } \right],\,Y = \alpha I + \beta X + \gamma {X^2}X=000100010,Y=αI+βX+γX2 and Z=α2I−αβX+(β2−αγ)X2Z = {\alpha ^2}I - \alpha \beta X + ({\beta ^2} - \alpha \gamma ){X^2}Z=α2I−αβX+(β2−αγ)X2, α\alphaα, β\betaβ, γ\gammaγ ∈\in∈ R. If Y−1=[15−2515015−250015]{Y^{ - 1}} = \left[ {\matrix{ {{1 \over 5}} & {{{ - 2} \over 5}} & {{1 \over 5}} \cr 0 & {{1 \over 5}} & {{{ - 2} \over 5}} \cr 0 & 0 & {{1 \over 5}} \cr } } \right]Y−1=51005−2510515−251, then (α\alphaα −-− β\betaβ + γ\gammaγ)² is equal to ____________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
