Prove that the set of all the quaternions, with the matrix addition and multiplication explained on pages 7 and 8, is a ring with unity. this ring is denoted by the symbol . find an example to show that is not commutative. (you may assume matrix addition and multiplication are associative and obey the distributive law.)

Which option identifies how kevin should proceed in the following scenario? four years ago kevin designed an mp3 player for young children. now that technology has changed, he would like to update his design to ensure that it encompasses cutting-edge techniques. by creating a third-angle projection of his ideas by designing an isometric projection of his new ideas by referring to past designs and illustrations of his original model by conferring with engineers who have improved upon similar devices