(a) The signature of the Commissioner of Education as such shall be sufficient indication of and shall validate his official action as commissioner.

(b) Whenever a statutory power or duty is or shall have been conferred or imposed upon the commissioner, such statutory power or duty shall be exercised or performed in the department by or under the direction of the commissioner for and in the name of the department.

(c) A statutory power or duty heretofore or hereafter assigned to the department, so far as the same is executive or administrative, shall be exercised or performed in the department by the commissioner, or by such agency or agencies of the department as he may designate.