Yulia

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.

casincal

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 clearly ,

Jeffrey Jordon