Assertion and reason

Exercise and reference answers

Questions

1. Reason

   A product needs the inner dimensions to agree, and swapping changes them.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   AB may exist while BA does not.

2. Reason

   (AB)′ = B′A′.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Transposing a product reverses the order of the factors.

3. Reason

   Its diagonal entries are all equal to the constant 1.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Every identity matrix is a scalar matrix.

4. Reason

   A scalar matrix has equal diagonal entries.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Every scalar matrix is an identity matrix.

Explanation