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True or false: transposes

Exercise and reference answers

Questions
  1. Statement is true
    Yes
    Statement
    (A′)′ = A.
  2. Statement is true
    Yes
    Statement
    (A + B)′ = A′ + B′.
  3. Statement is true
    No
    Statement
    (AB)′ = A′B′.
  4. Statement is true
    Yes
    Statement
    (AB)′ = B′A′.
  5. Statement is true
    Yes
    Statement
    (kA)′ = kA′.

Explanation

The transpose rules, with the product rule as the one that bites. Source: syllabus Maths Part I, Ch 3 Matrices.
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