I was hesitating somehow to post this answer, but the decision to post an answer comes from the fact that we had a quarter of beginning code, but which is not the way i would do the job.

**First** let us improve the given start to have a solution:

```
A = matrix( ZZ, [ [4, 1, 6], [1, 3, 9], [2, 7, 25] ] )
def sum_quadrate(A):
m = A.nrows()
n = A.ncols()
result = 0
for j in range (m):
for k in range(n):
entry = A[j, k]
if entry.is_square():
result += entry
return result
print sum_quadrate(A)
```

The above gives the `40`

as a result. And now the many comments. Please always use **four spaces** to indent. This is a good style, and saves a lot of troubles. In fact, we need only an access to the entries of $A$, so we need a "better way to loop". The suggestions of tmonteil already give the answer, so a better way to do the job...

... is the following way:

```
A = matrix( ZZ, [ [4, 1, 6], [1, 3, 9], [2, 7, 25] ] )
def sum_quadrate(A):
result = 0
for entry in A.list():
if entry.is_square():
result += entry
return result
print sum_quadrate(A)
```

Again we get that `40`

.
This is again not the best way to do the job. Instead...

... using **list comprehension** we can get some mathematically easily readable version of the function:

```
def sum_quadrate(A):
return sum([0]+[entry for entry in A.list() if entry.is_square()])
```

*Note:* The `[0]+`

part is needed for the case there is no perfect square in the list of entries of $A$.

A matrix=(4,1,6)(1,3,9)(2,7,25)