I have lived in my mothers home for 2 of the last 5 years but my mother passed away last year, so I have been the owner for only a few months. Would I owe capital gains tax if I sold the property for a gain now? Thanks.

It depends; The IRS states that you must report the sale of a home unless it was your primary residence.The tax law provides homeowners with a very generous tax exclusion when they sell their property. Up to $250,000 of any gain from such a sale received by a single homeowner is tax free. For married homeowners filing jointly, up to $500,000 of gain is excluded from income. To qualify for the exclusion, the home must have been used as a main home for two years out of the prior five years before the sale. For details see, the article "The $250k/$500k Home Sale Exclusion."
At the time you inherit a home, you won't qualify for this exclusion. You'd have to move into the home and live there for at least two years to qualify.