Mathematics I / Matrices and Matrix Operations
Practice question · True or false

For square matrices AA and BB of the same size, (AB)T=ATBT(AB)^{T} = A^{T}B^{T}.

Hints
  1. Transpose the product of a 2×3 and a 3×2 and check the shapes.
  2. The order has to reverse.
Show the answer

False

Why

False. The correct identity is (AB)T=BTAT(AB)^{T} = B^{T}A^{T}, the order reverses. For non-square matrices the wrong version does not even typecheck, and for square ones it silently gives a different matrix, since AB≠BAAB \neq BA in general. The same reversal appears in inverses: (AB)−1=B−1A−1(AB)^{-1} = B^{-1}A^{-1}.

Read the lesson: Matrices and Matrix Operations →

Practise Matrices and Matrix Operations

The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.

Start Mathematics I free Get it onGoogle Play

More questions on Matrices and Matrix Operations