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Let P be a n*n diagonalizable matrix which satisfies the equations Psqr=P,Tr(P)=n-1,then det(P) is?

Let P be a n*n diagonalizable matrix which satisfies the equations Psqr=P,Tr(P)=n-1,then det(P) is?

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1 Answers

robin singh sidhu
30 Points
9 years ago
let A square matrix A=[aij] aij=0 for all i not=j for i=j assume elements to be a1,a2,a3...n A(sqr)=[aij(sqr)] aij=0 for all i not=j. hence for i=j we get a1(sqr),a2(sqr),a3(sqr)....n corresponding to diagonal elements of A(PROP OF DIAGNAL MATRIX) tr(A)=n-1 and A=A(sqr) therefore , a1(sqr)=a1 a2=a2(sqr) and so on hence each diagnal element can be 0 or 1 but tr(A)=n-1 hence one of the elements shud be 0. det(A)=a1 x a2 x a3......n=o

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