Suppose A is a nonsingular n x n matrix (a) Prove that any n x (n k) matrix of the form (A B), where B has size n Atilde k has rank n (b) Prove that any (n k) Atilde n matrix of the form where C has size k Atilde n, has rank n A

Question: Suppose A is a nonsingular n x n matrix. (a) Prove that any n x (n + k) matrix of the form (A B), where

Suppose A is a nonsingular n x n matrix.
(a) Prove that any n x (n + k) matrix of the form (A B), where B has size n Ã— k. has rank n.
(b) Prove that any (n + k) Ã— n matrix of the form

where C has size k Ã— n, has rank n.

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