Let s say we have an algorithm that takes as input 3 matrix A,B and C

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

the algorith works as follow ;

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