Two are true, one is not

Exercise and reference answers

Questions

1. False statement

   AB = BA for all matrices

   Statements

   1. A + B = B + A
   2. A(BC) = (AB)C
   3. AB = BA for all matrices

2. False statement

   (AB)′ = A′B′

   Statements

   1. (AB)′ = A′B′
   2. (A′)′ = A
   3. (A + B)′ = A′ + B′

3. False statement

   Every square matrix is symmetric

   Statements

   1. A symmetric matrix satisfies A′ = A
   2. Every square matrix is symmetric
   3. A skew symmetric matrix satisfies A′ = −A

Explanation