A square northwest matrix B is zero in the southeast corner, below the antidiagonal that

Chapter 1, Problem 1.6.68

(choose chapter or problem)

A square northwest matrix B is zero in the southeast corner, below the antidiagonal that connects (1,n) to (n,1). Will B T and B 2 be northwest matrices? Will B 1 be northwest or southeast? What is the shape of BC = northwest times southeast? You are allowed to combine permutations with the usual L and U (southwest and northeast).

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