No, both brothers cannot claim the mother as a dependent. One of them might be able to. Generally, they may decide between them which one will claim her. They still need to meet all the dependent rules, but may apply the "multiple support" rule.
But, if they live in a house owned by the mother, there's a strong chance they don't meet the support rule.
A person can still be a Qualifying
relative dependent, if not a Qualifying Child, if he/she meets the 6 tests for
claiming a dependent:
1. Closely Related OR live
with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4,050 (2016)
3. The taxpayer must have
provided more than 1/2 his support (see multiple support exception below)
4. He must be a US citizen or resident of the US, Canada
or Mexico
5. He must not file a joint
return with his spouse or be claiming a dependent of his own
6. He must not be the
qualifying child of another taxpayer
Social security doesn't count
as income, for the income test, but social security money she spends on her
self does count as support not provided by you, for the support test. Money she
puts into savings & investment does not count as support she spent on
herself. Note that a parent is closely related so there is no requirement that
she live with you at any time, during the year. But if you provided a home it
helps your support case, unless they own the home you live in. If no one person
(or married couple) provides 50% of the support, including the mother herself, then a "multiple support agreement” (IRS Form 2120)
can be used, to allow you to claim the dependent. https://www.irs.gov/pub/irs-pdf/f2120.pdf
The IRS has a worksheet that
can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf The support
value of a home is the fair market rental value, divided by the number of
occupants.
