Let $$A = \left[\begin{array}{cccc} 0 &-1 &-4 &-1\cr -8 &0 &8 &4\cr -4 &0 &4 &2\cr -8 &-1 &4 &3 \end{array}\right].$$ Find orthonormal bases of the kernel and image of $A$.

Basis of the kernel:
$\Bigg\lbrace$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$, $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\Bigg\rbrace.$

Basis of the image:
$\Bigg\lbrace$ $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$, $\left[\Rule{0pt}{4.8em}{0pt}\right.$$\left]\Rule{0pt}{4.8em}{0pt}\right.$ $\Bigg\rbrace.$