Question: let A and B be two nxn matrices. A linear algebra professor asked whether rank of B and AB are the same if A has

let A and B be two nxn matrices. A linear algebra professor asked whether rank of B and AB are the same if A has full rank. What should be the answer? Justify.

If A

^2 =

,

^2 =

B and I

-

-

B is invertable then help the students to prove A and B are of same rank

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