When is a product defined?

Exercise and reference answers

Questions

1. Question

   For AB to be defined, the columns of A must match

   Choices

   1. the columns of B
   2. the rows of B
   3. nothing in particular

   Correct choice

   the rows of B

2. Question

   If A is m × n and B is n × p, then AB has order

   Choices

   1. n × n
   2. p × m
   3. m × p

   Correct choice

   m × p

3. Question

   Is AB = BA in general?

   Choices

   1. No
   2. Yes, always
   3. Only for row matrices

   Correct choice

   No

4. Question

   (AB)′ equals

   Choices

   1. A′B′
   2. B′A′
   3. AB

   Correct choice

   B′A′

Explanation