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Find a (simple ?) non-zero (2 2) matrix A and two vectors x and y such that Ax = Ay, but x = y. Find

Find a (simple ?) non-zero (2 2) matrix A and two vectors x and y such that Ax = Ay, but x = y.

Find two (simple ?) non-zero (2 2) matrices A and B such that AB = 0. ("Non-zero" means not all entries are zeros. Some entries are allowed to be zero.)

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