If X is a matrix of order 3\times3, Y is a matrix of order 2\times3 and Z is a matrix of order 3\times2, then which of the following are correct? 1. (ZY)X is a square matrix having 9 entries. 2. Y(XZ) is a square matrix having 4 entries. 3. X(YZ) is <strong>NOT</strong> defined. Select the correct answer using the code given below :

Explanation

Matrix Z (3 \times 2) multiplied by Y (2 \times 3) yields ZY as 3 \times 3. Multiplying by X (3 \times 3) makes (ZY)X a 3 \times 3 matrix with 9 entries (Statement 1 is true). X (3 \times 3) times Z (3 \times 2) gives XZ as 3 \times 2. Y(XZ) is then 2 \times 2 with 4 entries (Statement 2 is true). YZ is 2 \times 2, so X(YZ) with dimensions 3 \times 3 and 2 \times 2 cannot be multiplied (Statement 3 is true).

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