Find the error in the following proof that $2=1.$

Consider the equation a $=$ b$.$ Multiply both sides by a to obtain a$2=$ ab$.$ Subtract$$b$2$ from both sides to get a$2$b$2=$ ab$$b$2.$ Now factor each side, $($a $+$ b$)($a$$b$)=$b$($a$$b$),$ and divide each side by $($a$$b$)$ to get a$+$b $=$ b$.$ Finally, let a and b equal $1,$which shows that $2=$