MADEEASY Doubt Matrix

Question

If A is a Skew Symmetric MAtrix then A.A is_______

a)symmetric   b)skew-symmetric    c)Diagonal    d)nothing can be said

Answer 1

for skew symmetric : A=-$A^T$

(A).A=$-A^T$.A

(A).A=$-A^T$.$-A^T$

A.A=$A^T$.$A^T$

A.A=$(A.A)^T$   (property of symmetric matrix)

hence A.A is symmetric

Comments

Hey guys. For skew symmetric, the diagonal elements are zero. Hence, A.A is a diagonal matrix. CHeck it.

Answer 2

I am getting SKEW_SYMMETRIC but answer is symmetric how?

Comments

you are correct ...

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But is it true for all other matrix too?

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sorry, for n=2, it is skew- symm.

but, for n=3, it may not be kew-symm.

So, nothing can be said .. right srestha ??

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yes .