Let X be a matrix of order 3\times3, Y be a matrix of order 2\times3 and Z be a matrix of order 3\times2. Which of the following statements are correct? I. (ZY)X is defined and is a square matrix of order 3. II. Y(XZ) is defined and is a square matrix of order 2. III. X(YZ) is <strong>NOT</strong> defined. Select the answer using the code given below.
- A. I and II only
- B. II and III only
- C. I and III only
- D. I, II and III ✓
Correct Answer: D. I, II and III
Explanation
Z_{3\times 2} and Y_{2\times 3} gives ZY as 3\times 3. So, (ZY)X is 3\times 3. X_{3\times 3} and Z_{3\times 2} gives XZ as 3\times 2. Thus Y(XZ) is 2\times 2. Since Y_{2\times 3} and Z_{3\times 2} gives YZ as 2\times 2, X(YZ) has incompatible dimensions 3\times 3 and 2\times 2, hence it is not defined.
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