Zero Divisors If a and b are real or complex numbers such thal ab =...

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 $n\times n$ matrices such that AB = 0 then it need not imply that either A =0 or B = 0.
Step 2
Counter example:
Take $A=\left(\begin{array}{cc}0& 1\\ 0& 0\end{array}\right)\text{ and }B=\left(\begin{array}{cc}0& 0\\ 1& 0\end{array}\right)$ clearly ,

$A\ne 0\text{ and }B\ne 0$

$\text{But }AB=0$

Answer is given below (on video)