Consider a crude extract with a mixture of the $5$ proteins listed below.

Protein A $4\mathrm{.}5$ pI $160$ molecular weight, kDa

Protein $$B $12\mathrm{.}5$ pI $$and $65$ molecular $$weight

Protein C $5\mathrm{.}0$ pI$,15$ molecular weight

Protein D $6\mathrm{.}8$ pI$,150$ molecular weight

Protein E $9\mathrm{.}5$ pI$,45$ molecular weight

You load this protein mixture onto an anion exchange column at pH $11.$

Next, you apply a "washing" step by passing through buffer at pH $11.$

Finally, for your elution step, you apply a pH gradient starting from pH $11$ to pH $2\mathrm{.}0.($A gradient buffer system allows you to gradually and continuously change the pH of your mobile phase starting from pH $11$ up to pH $2).$ You load this same protein mixture onto a Size Exclusion column. Please indicate the order in which these proteins will elute for both. If your protein of interest is protein A$,$ would using anion exchange column be completely successful at separating it from all the other proteins? Please explain.