## True or False Problems on Midterm Exam 1 at OSU Spring 2018

## Problem 702

The following problems are True or False.

Let $A$ and $B$ be $n\times n$ matrices.

**(a) **If $AB=B$, then $B$ is the identity matrix.

**(b)** If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions.

**(c)** If $A$ is invertible, then $ABA^{-1}=B$.

**(d)** If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix.

**(e)** If $x_1=0, x_2=0, x_3=1$ is a solution to a homogeneous system of linear equation, then the system has infinitely many solutions.