99 Percentile Qs Bank for JEE MainMathematicsMatrices

P is a 3 3 square matrix and Tr (P) 0 . If Tr ( P - P ^ T )+ Tr ( P + P ^ T )+ Tr (P) Tr (P^T ) + Tr ( P ) Tr ( P ^ T )= 0 then Tr ( P )=

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Correct answer

B. -1

Step-by-step solution

Tr (P)= Tr (P_T ) aligned & Tr (P-P^T )+ Tr (P+P^T )+ Tr (P) Tr (P^T ) + Tr (P) Tr (P^T )=0 & 0+2 Tr (P)+1+ Tr (P)^2=0 & ( Tr (P))^2+2 Tr (P)+1=0 & ( Tr (P)+1)^2=0 Tr (P)+1=0 & Tr (P)=-1 . aligned

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