True/False: Let be a square matrix. If then is invertible.

True/False: Let be an matrix. If then is invertible.

If is a matrix with a two-dimensional null space, what is the rank of
?

If is a matrix with , what is ?

If is a matrix with , what is the rank of ?

If is a matrix with , what is the rank of ?

and below are row equivalent. Determine the following values.

A basis for is