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the matrix

1 -1

1 -1

has the property that A^{2}=0. Is it possible for a nonzero symmetric 2x2 matrix to have this property? Prove your answer.

my work:

for a 2x2 matrix A to be its own inverse, it has to have the form

a b

b a

This squared is

(a^{2}+ b^{2}) (2ab)

(2ab) (a^{2}+ b^{2})

(things in parenthesis are their own elements -- it wont save the spaces)

Because there are no real numbers so that a^{2}+ b^{2}= 0, there is no 2x2 symmetric matrix that has its square equal to the zero vector.

edit: ^^ other than a = 0, and b = 0, which would be a 2x2 zero matrix -- something taken to account in the statement of the question

Is this right? My book doesnt have a solution for this one

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# Homework Help: Applied Linear Algebra problem

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