20. Let the equation of ellipse E be $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$. Let O be the origin, point A has coordinates $( a , 0 )$, point B has coordinates $( 0 , b )$. Point M is on the line segment AB and satisfies $| B M | = 2 | M A |$. The slope of line OM is $\frac { \sqrt { 5 } } { 10 }$. (1) Find the eccentricity $e$ of E; (2) Let point C have coordinates $( 0 , - \mathrm { b } )$, and N be the midpoint of segment AC. Prove that $\mathrm { MN } \perp \mathrm { AB }$.
20. Let the equation of ellipse E be $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > b > 0 )$. Let O be the origin, point A has coordinates $( a , 0 )$, point B has coordinates $( 0 , b )$. Point M is on the line segment AB and satisfies $| B M | = 2 | M A |$. The slope of line OM is $\frac { \sqrt { 5 } } { 10 }$.\\
(1) Find the eccentricity $e$ of E;\\
(2) Let point C have coordinates $( 0 , - \mathrm { b } )$, and N be the midpoint of segment AC. Prove that $\mathrm { MN } \perp \mathrm { AB }$.