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Let A and B be nxn matricies such that AB is singular. Prove that either A or B is singular.

Sooooo, here we go.

Let M = AB where is M is the given singular matrix.

Becuase M is singular then

M

**x**=0 has an infinite amount of solutions.

Let J be one of the non zero solutions

M

**j**=0

AB

**j**=0

this is where I get stuck.

If knew that B was singular I think I could prove M is singular but I am having trouble from this way around.

Any ideas?