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Let X be a matrix of order 3 3, Y be a matrix of order 2 3 and Z be a matrix of order 3 2 . Which of the following statements are correct? A. ( ZY ) X is defined and is a square matrix of order 3 . B. Y ( XZ ) is defined and is a square matrix of order 2. C. X ( YZ ) is not defined. Select the answer using the code given below.

Options

  1. AA and B only
  2. BB and C only
  3. CA and C only
  4. DA , B and C

Correct answer

D. A , B and C

Step-by-step solution

Since we know that matrix multiplication is only possible when column of first matrix is equal to row of the second matrix. A_ m n B_ n p =(A B)_ m p Thus [ Z _ 3 2 Y _ 2 3 ] X _ 3 3 =( zyx )_ 3 3 and Y _ 2 3 [ X _ 3 3 Z _ 3 2 ]=( yxz )_ 2 2 and x _ 3 3 [ Y _ 2 3 Z _ 3 2 ]= X _ 3 3 ( YZ )_ 2 2 No. of columns in X = no. of rows in ( yz ) Hence x(y z) is not defined.

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