Numpy multiply arrays into matrix (outer product)

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I have 2 numpy arrays of shape (5,1) say: a=[1,2,3,4,5] b=[2,4,2,3,6]

How can I make a matrix multiplying each i-th element with each j-th? Like:

..a = [1,2,3,4,5]
b 
2    2, 4, 6, 8,10
4    4, 8,12,16,20
2    2, 4, 6, 8,10
3    3, 6, 9,12,15
6    6,12,18,24,30

Without using forloops? is there any combination of reshape, reductions or multiplications that I can use?

Right now I create a a*b tiling of each array along rows and along colums and then multiply element wise, but it seems to me there must be an easier way.

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