# prove a property

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Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.

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!

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We do not do other people's homework for them. Please show some attempt at an answer and explain here you are stuck.

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22 hours ago, hypervalent_iodine said:
!

Moderator Note

We do not do other people's homework for them. Please show some attempt at an answer and explain here you are stuck.

Its not a homework, lol. Just an interesting problem, that i don't quite understand. I think that the only option is that A matrix is zero matrix or maybe i have forgotten some theorem  or criteria

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• 3 weeks later...

Well, as stated the first part has only one solution, the zero matrix; on the other hand the zero matrix is skew-symmetric..

The first part could be modified but why bother, its gonna be a rotation of $$\pi/2$$ radians in some direction, i.e. the solution space could be visualized as a circle with every point a matrix.

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