From my Linear Algebra class (ungraded) pratice work:  "If AB is a defined product of matrices A and B, and the columns of AB are linearly independent, is it necessarily the case that the columns of B are also linearly independent?"   So I got this far: (AB)x = 0 has only the trivial solution by the associative law of multiplication, (AB)x = A(Bx) = 0    from here, I'm not sure how to show the columns of B must be linearly independent.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.