90. If an *n* x *n* matrix T is an upper triangular, idempotent matrix with the first *k*

diagonal elements equal to unity and the remaining diagonal elements equal to zero and T is partitioned so that T =

[T₁₁ T₁₂

0 T₂₂]

where T₁₁ is a *k* x *k* matrix, show that T₁₁ = I, T₂₂ = 0, and T₁₂ is arbitrary.