Orders of matrix products

Orders of matrix products

Secondary 3
4 marks
TGM Original Questions

Matrices A, B and C have orders \(2\times3\), \(3\times1\) and \(2\times2\) respectively.

  1. State whether each product \(AB\), \(BA\) and \(CA\) exists. Give the order of each product that exists.[3]
  2. Explain why \(AC\) does not exist.[1]

Solution:

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Answer:(a) \(AB:2\times1\); BA undefined; \(CA:2\times3\). (b) Inner dimensions 3 and 2 differ.

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