Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions

1. Question

   Three of these statements about matrix products are false.

   Choices

   1. Item

      AB needs columns of A to match rows of B

      Correct

      Yes

   2. Explanation

      Matrix multiplication is not commutative.

      Item

      AB = BA always

   3. Explanation

      Their orders must still agree with each other.

      Item

      AB exists for any two square matrices

   4. Explanation

      It is rows of A by columns of B.

      Item

      AB has the order of A

2. Question

   Three of these statements about inverses are false.

   Choices

   1. Item

      If AB = BA = I then B is the inverse of A

      Correct

      Yes

   2. Explanation

      Only some square matrices do.

      Item

      Every matrix has an inverse

   3. Explanation

      The inverse, when it exists, is unique.

      Item

      A matrix may have two different inverses

   4. Explanation

      The transpose is not generally the inverse.

      Item

      The inverse of A is A′

Explanation