Skew-symmetric matrices problem ?

[ngkamsengpeter]

Homework Statement

Give an example of two skew-symmetric matrices. Show explicitly that they display the property of skew-symmetry, ie, AB = -BA

Homework Equations

The Attempt at a Solution

transpose of (AB) = BA
I just can show that AB=BA but can't show AB=-BA .
Is it (-A)(-B)=AB ?

 

[Dick]

The defining property of a skew-symmetric matrix is transpose(A)=-A. So yes, transpose(AB)=(-B)*(-A)=BA. Beyond that I simply don't follow you. A=[[0,1],[-1,0]]. B=transpose(A)=[[0,-1],[1,0]]. AB=1=BA. AB is not equal to -BA. AB=-BA is property of anticommuting matrices.

 

[chanvincent]

Since AB=BA, AB can't be -BA unless AB = 0

 

[HallsofIvy]

Since AB=BA, AB can't be -BA unless AB = 0

Nonsense. Multiplication of matrices is NOT in general commutative.

 

[ngkamsengpeter]

I think i have misunderstood the questions. My lecturer say the question is we multiply any 2 matrices to get a skew-symmetry matrix AB . Then show that AB=-BA . But i simply can't show it .
I even don't know how to give 2 matrices where the product of these 2 matrices is skew-symmetry matrix .
I know i can use try but i think that is not a good and standard technique .
Anybody has any idea on this question?

 

[Dick]

A=[[-1,-1,0],[0,1,1],[-1,0,1]], B=[[0,1,0],[0,0,1],[1,0,0]].

AB is skew symmetric. AB is not equal to -BA. No wonder you can't show it. Do you mean to add the assumption A and B are symmetric?