Question

Which is the following is true about addition of matrices.

• A. Addition of matrices can be performed only on two matrices of the same orders.
• B. Addition of matrices can be performed on two matrices which are not necessarily of same order.
• C. The resultant matrix obtained after addition of two matrices is of the same order as the order of two original matrices.
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A

Addition of matrices can be performed only on two matrices of the same orders.

C

The resultant matrix obtained after addition of two matrices is of the same order as the order of two original matrices.

If A and B are two matrices, the A + B will be obtained by addition of corresponding elements of two matrices like $1^{st}$ element of $1^{st}$ row of A should be added to $1^{st}$ element of $1^{st}$ row of B, second element of first row of A should be added to second element of first row of B and so on. Don’t you think this is possible only when two matrices have the same order? If this is not the case then think of adding a matrix of 3 $\times$ 3 order to a matrix of the order 2 $\times$ 2. To what element of the second matrix will you add the third element of third row of the first matrix? There is no corresponding element. So, they have to have the same order for that to happen. Also the resultant matrix will have same number of rows and columns. Rightly so as all the elements are made by addition of corresponding elements of A & B, so a &c are correct options.