show that for all A,B nxn matrices over the field F:
a)trace(X+Y)=trace(X) + trace(Y)
b)trace(XY)=trace(YX)
c)show that there are no nxn matrices X,Y such that XY-YX= indentity martrix
show that for all A,B nxn matrices over the field F:
a)trace(X+Y)=trace(X) + trace(Y)
b)trace(XY)=trace(YX)
c)show that there are no nxn matrices X,Y such that XY-YX= indentity martrix
a) follows from the definition of matrix addition,