Consider the following binary operations on $R^4$ :

$o+$:$R^4{R}^4{R}^4$

$((a_1,a_2,a_3,a_4),(b_1,b_2,b_3,b_4))|(a_1+b_1,a_2+b_2,a_3+b_3,a_4+b_4)$

$ox$:$R^4{R}^4{R}^4$

$((a_1,a_2,a_3,a_4),(b_1,b_2,b_3,b_4))|(a_1{b}_1+a_2{b}_3,a_1{b}_2+a_2{b}_4,a_3{b}_1+a_4{b}_3,a_3{b}_2+a_4{b}_4)$

$($a$)$ Show that $ox$ is distributive over $o+.$

$($b$)$ Show that there is a neutral element for $ox.$