If a is invertible, then the columns of upper a superscript negative 1 are linearly independent. explain why. select the correct choice below.
a. it is a known theorem that if a is invertible then upper a superscript negative 1 must also be invertible. according to the invertible matrix theorem, if a matrix is invertible its columns form a linearly independent set. therefore, the columns of upper a superscript negative 1 are linearly independent.
b. if a is invertible, then the rows of a are linearly independent, which implies that the columns of upper a superscript negative 1 are linearly independent.
c. the columns of upper a superscript negative 1 are linearly independent because a is a square matrix, and according to the invertible matrix theorem, if a matrix is square, it is invertible and its columns are linearly independent.
d. according to the invertible matrix theorem, if a matrix is invertible its columns form a linearly dependent set. when the columns of a matrix are linearly dependent, then the columns of the inverse of that matrix are linearly independent. therefore, the columns of upper a superscript negative 1 are linearly independent.