82 Proceedings of Royal Society of Edinburgh. 
And, conversely, if 
11 
12 
13 • 
■ • 1 n 
21 
22 
23 • • 
■ • 2 n 
rl 
r'2 
r3 • 
• • rn 
where A is a determinant of the n th or r th order, then 
11 
12 
13 . • 
• 1 n 
21 
22 
23 • • 
• 2 n 
| rl 
r2 
r3 • • 
• rn 
provided that A ^0. 
