MHB Proving A is Zero Matrix if B is Invertible & Same Size as A

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Show that if A and B are square matrices of the same size such that B is an
invertible matrix, then A must be a zero matrix.
 
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blueman11 said:
Show that if A and B are square matrices of the same size such that B is an
invertible matrix, then A must be a zero matrix.
We need information about how A and B are related. ie. AB = 0 or something.

-Dan
 

Thread 'The colorful world of ##2\times 2## complex matrices'

The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...
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