Let a hnn show that if there exists b hnn such that ba i

Question

Question: Let A ∈ H^n×n. Show that if there exists B ∈ Hn×n such that BA = I, then A is invertible and B = A-1.

Repeat above, with BA = I replaced by AB = I. The row rank of a matrix A ∈ H^m×n is defined as the dimension of the (left quaternion) subspace spanned by the rows of A. Show that the row rank of A coincides with rank (A).