Correct Answer - Option 3 : 3 × 3 and 5 × 5
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.
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
The order of BA = number of row is B × number of columns in A
= 5 × 5
Hence, option (3) is correct.