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If A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3, then the order of AB and BA will respectively be
1. 3 × 3 and 3 × 3
2. 3 × 5 and 5 × 3
3. 3 × 3 and 5 × 5
4. 5 × 3 and 3 × 5
5. None of these

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Correct Answer - Option 3 : 3 × 3 and 5 × 5

Concept:

For multiplication of two matrices: 

  • The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.
  • The result will have the same number of rows as the 1st matrix, and the same number of columns as the 2nd matrix.
  • Example: To multiply an "m × n" matrix by " l × p" matrix, the n must be the same as I, and the result will be "m × p" matrix.

Calculation:

Given: A is a matrix of order 3 × 5 and B is a matrix of order 5 × 3

Number of rows in A = 3

Number of column in A = 5

Number of rows in B = 5

Number of column in B = 3

The order of AB = number of row is A × number of columns in B

= 3 × 3

And, 

The order of BA = number of row is B × number of columns in A

= 5 × 5

Hence, option (3) is correct.

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