If the matrix  $AB$ is zero, then 

$A=O\text{\hspace{0.17em}\hspace{0.17em}or\hspace{0.17em}\hspace{0.17em}}B=O$

$A=O\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}B=O$

It is not necessarily that either  $A=O\text{\hspace{0.17em}\hspace{0.17em}or\hspace{0.17em}\hspace{0.17em}}B$ should be zero

All the above statements are wrong