Introduction to Linear Algebra, Section 4.2, Problem 34:
"If A har r independent columns and B has r independent rows, AB is invertible"

How can AB be invertible if it's not necessarily square?
Do I understand the problem wrong?

Question

Introduction to Linear Algebra, Section 4.2, Problem 34:
"If A har r independent columns and B has r independent rows, AB is invertible"

How can AB be invertible if it's not necessarily square?
Do I understand the problem wrong?

anonymous · Answer

Your right in that a matrix must be square in order to be invertible.  Assuming this is a true-false question, it is quite simple to find a counter example in this case, the only given is that the matrices CAN be multiplied together since the columns in the first match the rows in the second.  Simply showing that the product of the two is not square is sufficient to answer the question.