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

Yulia

Answered question

2021-03-02

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.

Answer & Explanation

casincal

casincal

Skilled2021-03-03Added 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

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-22Added 2605 answers

Answer is given below (on video)

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