Let U E Rnxn be upper-triangular and with non-vanishing diagonal entries, i.e. Ui ‡ 0 for all i € [n]. Show that U is invertible, U-¹ is also upper-triangular, and (U−¹) ii 1 = Uii Hint: recall that the inverse matrix is unique if it exists. Try to construct an upper- triangular matrix V with Vi= 1 and such that UV = I.
