Zero Divisors If a and b are real or complex numbers such thal ab = O. then either a = 0 or b = 0. Does this property hold for matrices? That is, if A and Bare n x n matrices such that AB = 0. is il true lhat we must have A = 0 or B = 0? Prove lhe resull or find a counterexample.

Yulia 2021-03-02 Answered
Zero Divisors If a and b are real or complex numbers such thal ab = O. then either a = 0 or b = 0. Does this property hold for matrices? That is, if A and Bare n x n matrices such that AB = 0. is il true lhat we must have A = 0 or B = 0? Prove lhe resull or find a counterexample.
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casincal
Answered 2021-03-03 Author has 82 answers

Given: "If a and b are real or complex numbers such thal ab = 0. then either a = 0 or b = 0"
No, the above property does not hold for matrices.
That is, if A and B are n×n matrices such that AB = 0 then it need not imply that either A =0 or B = 0.
Step 2
Counter example:
Take A=(0100) and B=(0010) clearly ,

A0 and B0

But AB=0

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Jeffrey Jordon
Answered 2022-01-22 Author has 2064 answers

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