Matrix multiplication randomised verification - error probability Let s  say we have an algorithm that takes as input 3 matrix A,B and C


  $$ \text{Input} :A,B,C \in Mat(n\times n)$$
  $$\text{Question} :\text{is } A\cdot B=C$$


the algorith works as follow ; 

$$ \text{if }(A\cdot B)_{ij}=C_{ij} \Rightarrow A\cdot B=C  $$
$$ \text{if }(A\cdot B)_{ij} \neq C_{ij} \Rightarrow A\cdot B \neq C  $$

with random chosen $i$ and $j$  .

I have to find in this case the error probrabilty. Can someone please give me some hints.

This problem looks a bit like  the freivalds algorithm, somehow i think i have to drive a trick with it so solve mine but i am not sure .
If that's the whole algorithm, only one iteration, then the only bound on the probability of error you can get is that it is smaller than $1-1/n^2$.

Hint 1) Notice that the algorithm only can fail when it enters in the first case you describe, why?

Hint 2) What is the worst possible case for A, B and C so you get the worse probability of error?