The cross product of two vectors in ℝ3 is defined by
⎡⎣⎢⎢a1a2a3⎤⎦⎥⎥×⎡⎣⎢⎢b1b2b3⎤⎦⎥⎥=⎡⎣⎢⎢a2b3−a3b2a3b1−a1b3a1b2−a2b1⎤⎦⎥⎥.
Let v⃗=⎡⎣⎢⎢45−3⎤⎦⎥⎥. Find the matrix A of the linear transformation from ℝ3 to ℝ3 given by T(x⃗)=v⃗×x⃗.

A= ⎡⎣⎢⎢⎢⎢⎢⎢ ⎤⎦⎥⎥⎥⎥⎥⎥