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If A, B, and C are any three square matrices of order (dimension) 3, then which of the following is true?
A + (B + C) = (A + B) + C
A (B + C) = AB + AC
(AB)C = A(BC)
All of the choices

Respuesta :

Answer: D) All of the choices

In other words, all of the above.

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Explanation:

Since matrix A, B, and C are all the same size (3 by 3), this means we can add them. Addition is defined. Multiplication is also defined in this case.

A few of the many properties of matrix addition and multiplication are

  • Matrix addition is associative, meaning A+(B+C) = (A+B)+C so we can group the matrices however we want.
  • Matrix multiplication is also associative, so A*(B*C) = (A*B)*C
  • Matrix distribution is possible: A*(B+C) = A*B+A*C

Keep in mind that the last property is not the same as (B+C)*A because the order of multiplication matters. A*B is not the same as B*A.

Based on those points above, we can see that all statements your teacher mentioned are true ones.

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