Well I'm working on matrices, and this thing is bugging me , though according to me it should be true because: let there be a nxn matrix:(aij ; i=row number, j=column number)
a11 a12 a13.....a1n a21 a22 a23...... a31 a32 a33...... . . . ...... . . . ...... an1 an2 an3......
then A^2 will be:
1 column 1 column 2 a11*a11+a12*a21+a13*a31....+a1n*an1|a11*a12+a12*a22+a13*a32....+a1n*an2| a21*a11+a22*a21+a23*a31....+an2*an1|a21*a12+a22*a22+a23*a32....+an2*an2| . |. | . |. | . |. | an1*a11+an2*a21+an3*a31....+ann*an1|an1*a12+an2*a22+an3*a32....+ann*an2|
so if we take the row elements to be constants x,y,z,..... then all the columns are essentially x*column1+y*column2............ What do you all think?