1. 


A 23 matrix has three columns and two rows. 
2. 


The transpose of a 56 matrix has five columns and six rows. 
3. 


If A is a 23 matrix and B is a 32 matrix, then A+B is defined. 
4. 


If A is a 23 matrix and B is a 32 matrix, then AB is defined. 
5. 


If A is a 23 matrix and B is a 32 matrix, then AB is defined. 
6. 


If A is a 34 matrix and B is a 34 matrix, then A+B is defined. 
7. 


If A is a 34 matrix and B is a 34 matrix, then AB is defined. 
8. 


If A is an invertible 33 matrix and B is a 34 matrix, then A^{1}B is defined. 
9. 


It is never true that A+B, AB, and AB are all defined. 
10. 


If AB is defined, then BA must also be defined. 
11. 


If AB and BA are both defined, they may have different dimensions. 
12. 


If AB and BA are both defined and have the same dimensions, then they are equal. 
13. 


If AX = B for any matrix A, then X = A^{1}B. 
14. 


If AX = B for a square matrix A, then X = A^{1}B. 
15. 


If AX = B for an invertible matrix A, then X = A^{1}B. 
16. 


The most efficient way to solve AX = B is to invert A. 
17. 


Every matrix none of whose entries are zero is invertible. 
18. 


Every invertible matrix is square and has no two rows the same. 
19. 


If one sector of the economy uses none of the products of another sector, then any increase in demand for the products of the first sector will have no effect on the second sector. 
20. 


You can see the complete effect of one sector on another only by looking at the whole economy. 