When -LSB- math -RSB- p -LSB- / math -RSB- is a prime and -LSB- math -RSB- a , b -LSB- / math -RSB- are integers , -LSB- math -RSB- -LRB- p \ mid ab -RRB- \ Rightarrow -LRB- p \ mid a -RRB- \ lor -LRB- p \ mid b -RRB- -LSB- / math -RSB- . What is the meaning of this theorem ?
What are two infinite nilpotent matrices A and B , for which the product AB is not nilpotent ?