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The question was strictly asking how to perform all add-one operations at once. (That print command was of course misplaced in the inner most loop.)
An answer constructs the B-copy already with the right entries. For me works best:
A = random_matrix( QQ, 5, 5 )
B = matrix( QQ, 5, 5, [ A[n,k]+1 for n in range(5) for k in range(5) ] )
print A
print B
