Question

If `P=[{:(x,0,0),(0,y,0),(0,0,z):}]` and `Q=[{:(a,0,0),(0,b,0),(0,0 ,c):}]` then prove that
`PQ=[{:(xa,0,0),(0,yb,0),(0,0,zc):}]=QP`.

Answer 1

`PQ=[{:( x,0,0),(0,y,0),(0,0,z):}][{:(a,0,0),(0,b,0),(0,0, c):}]=[{:(xa,0,0),(0,yb,0),(0,0,zc):}]`
and `QP=[{:(a,0,0),(0,b,0),(0,0,c):}] [{:(x,0,0),(0,y,0),(0,0,y):}]=[{:(ax ,0,0),(0,by,0),(0,0,zc):}]`
Thus, we see that `PQ=QP`