# 1. The 3rd row, 4th column entry of a matrix is below and to the right

```1.
The 3rd row, 4th column entry of a matrix is below and to the right of the 2nd
row, 3rd column entry. T
2.
A matrix with dimensions m&times;n, where m &gt; n, has fewer rows than columns. F
3.
The ith row, jth column entry of a square matrix, where i &gt; j, is called a diagonal
entry. F
4.
If the corresponding entries of two matrices A and B with the same dimensions
are equal, then A = B. T
5.
For any matrix A, there exists a matrix B so that A + B = 0. T
6.
For any matrix A, 2A + 3A = 5A. T
7.
For any matrices A and B, 3(A + B) = 3A + 3B. T
8.
If matrices A and B have the same dimension, then A + B = B + A is known as
the Associative Property for Addition of Matrices. F
9.
If A has dimensions m &times;r and B has dimensions r &times;n , then AB has dimensions
r&times;n. F
10.
If A has dimensions m &times;n and B has dimensions n &times; r, then AB has dimensions
m&times;r. T
11.
If A has dimensions 5 &times;4 and B has dimensions 4 &times;3, then the 3rd row, 4th
column entry of AB is obtained by multiplying the 3rd column of A by the 4th
row of B. F
12.
If AB is defined, then BA is also defined. F
13.
If AB has dimensions k&times;p, then the number of rows of A is p. F
14.
If A is a square matrix such that A⋅A equals the 0 matrix, then A must equal the 0
matrix. F
15.
If A and B are both square matrices such that AB equals BA equals the identity
matrix, then B is the inverse matrix of A. T
16.
If A is a square matrix, then there exists a matrix B such that AB equals the
identity matrix. F
17.
If AX = B represents a system of linear equations and A-1 exists, then the
product A-1 B gives the solution to the system. T
```