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Problem related to coinciding os ranks

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Question: Let A ∈ Hn×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 ∈ Hm×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).

Reference no: EM131587521

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