(VECTORS/MATRICES) calculating the projection of 2 edges of a cube

red box:

is this a generic matrix? so every time i need to find the perspective projection of line segments i should use this?

brown box:
i multipled the matrix of coordinates (1 0 5 | 1 0 10 | 1 5 5 | 1 5 10) by the homogeneous matrix (1 0 0 0 | 0 1 0 0 | 0 0 1 1 | 0 0 0 0) to get (1 0 5 | 1 0 10 | 2 10 15 | 0 0 0)

so when i normalise i should have 1/sqrt(26), 0, 5/sqrt(26) for the first column but the answer gives (1/5, 0, 1, 1)

where did i go wrong? thanks in advance for any help, it's highly appreciated

The matrix in the red box is the identity matrix.

The identity matrix has 1s in the diagonal. This cannot be the identity matrix.

Opp's didn't see that 0 at the end.

Not something I've studied, but this (or just the statement at its end) may be useful regarding the brown box.

Opp's didn't see that 0 at the end.

Or the 1 at the bottom second from the right? :P