Standard Matrix of Linear Transformation

[renolovexoxo]

Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.

 

[pka]

Let T: R3-->R3, defined by T(x)= a x x
Give the standard matrix A of T, and explain why A is skew-symmetric.

Suppose that A=<a,b,c> then
T(A)=[0, -c, b; c, 0, -a; -b, a, 0] WHY?