Question: Let A be a 4 6-matrix and let B be a 6 4-matrix. Then both AB and BA are square matrices. (a) Show that null(

Let A be a 4 6-matrix and let B be a 6 4-matrix. Then both AB and BA are square

matrices.

(a) Show that null(A) = {0}.

(b) Prove that BA is not invertible.

(c) Give an example of a 4 6-matrix A and a 6 4-matrix B for which AB = I4, the

4 4 identity matrix.

(d) Is it true that, for any 4 6-matrix A and any 6 4-matrix B, we have det(AB) =

det(BA)?

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