Question: True or False, the product of two linear independent matrices is linear independent. (assuming the matrices can be multiplied) Provide a full proof or counter example.
Yes, the problem is referring to the rows/columns being independent. It refers to the matrices as "vector sets" so I assume its actually talking of columns. This would mean their determinants cannot equal zero, but how can this help, would i set up two matrices of this type and show that the det cannot equal zero?