Q:

Is this just a nested For Loop? 

Came across this code the other day:
for(i=0; i<r1; ++i)
for(j=0; j<r1; ++j)
for(k=0; k<r1; ++k){
    mult[i][j] += a[i][k] * b[k][j];
}

Now, is this just a different way of writing:
for(i=0; i<r1; ++i){
    for(j=0; j<r1; ++j){
        for(k=0; k<r1; ++k){
            mult[i][j] += a[i][k] * b[k][j];
        }
    }
}

A:

yes that is correct .. Put brackets around the first implementation to see for yourself. 
PS - there is no one right way  .. but I would highly recommend using brackets always ( especially if you are new to programming ) . 
It goes a long way to help you understand and debug the code

