How Does Row Reduction Show that det(H) = 0 for Matrix H = Q - nI?

[j3n]

PLEASE HELP! a matrix proof..

Hey!

I really need help with this question if possible.

Let Q be an n x n matrix with each entry = 1
Let I be the n x n identity matrix
let H = Q-n*I
show that det(H) = 0

(hint: think of row reducing H)

Thanks a lot,
j3n

 

[HallsofIvy]

The hint pretty much tells you what to do. This might help: What is the sum of each column?