Determine the taxable income and income tax payable for the following situation:

Luke sold his primary residence on January $31,2021,$ for $$433,000.$ He purchased the home in $2006$ for $$184,000$ and installed a new garage on the property at a cost of $$27,000$ in $2010,$ replaced his roof in $2012$ for $$8,000,$ and repainted the home in $2018$ for $$1,200.$ When Luke sold his home in January, the realtor kept $6\%$ of the sales price for commissions. In addition to the commission, Luke paid a transfer tax of $$2,200,$ a state filing fee of $$150,$ and $$350$ for property taxes associated with the home for the period of $1/1/21$ to $1/31/21.$

On December $12,2020,$ Luke$$s father, Gerry, passed away and bequeathed his home to Luke. Gerry had paid $$96,000$ for his beachfront home in $1956.$ Gerry was considering selling the home prior to his death and had received a Brokers Pricing Opinion $($BPO$)$ on December $3$ of $2020$ that valued his home at $$1,236,000.$ After Gerry$$s death, Luke was unable to obtain any records that indicated any work being conducted on Gerry$$s house. After Luke sold his home, he moved into his inherited house on $2/1/21$ and started living there as his primary residence. After living in the home for several months, Luke decided he didn$$t feel comfortable there and decided to sell the home. On November $28,2021,$ Luke sold the home for $$1,325,000.$ The realtor kept $6\%$ of the sales price of the home for commission and Luke paid a transfer tax of $$2,500,$ a state filing fee of $$150,$ and $$8650$ for property taxes associated with the home for the period of $2/1/21$ to $11/28/21.$ What is the gain$/$loss and taxable income on each property sold and the income tax associated with each property? Assume Luke has a capital gains rate of $20\%.$

$*$Reference the Internal Revenue Code using in$-$text citations to justify all determinations that you make.