using LinearAlgebra

A = rand(4,4)

Q,R  = qr(A)

round.(Q'Q, digits=0)

round.(Q*Q', digits=0)

A ≈ Q * R

Q * R

A

A = rand(5,3)

Q,R = qr(A)
Q = Q[:,1:3] # make sure we have the first three columns

Q

R

Q * R

A

A ≈ Q * R

round.(Q'Q, digits=0)

Q * Q'