Science:Math Exam Resources/Courses/MATH152/April 2011/Question A 27/Statement

Which of the following statements are true for all invertible $n\times n$ invertible matrices $A$:

• (a) $A$ has rank $n$.
• (b) The reduced row echelon form of $A$ is the identity matrix.
• (c) The homogeneous problem $A\mathbf {x} =0$ has only the trivial solution $\mathbf {x} =0$.
• (d) $A$ does not have $\lambda =0$ as an eigenvalue.
• (e) $\det(A)\not =0$.