This new matrix is the sum of the above two matrices We observe that the sum of two matrices is a matrix obtained by adding the corresponding elements of the given matrices Furthermore the two matrices have to be of the same order Thus if A 2 3 matrix Then we define A B Example 6 911 912 913 921 922 923 is a 2 x 3 matrix and B and is given by A B In general if A a and B b are two matrices of the same order say m n Then the sum of the two matrices A and B is defined as a matrix C c a b for all possible values of i and j 3 1 1 Since A B are of the same order 2 3 0 and B she a 1 b a 2 b 2 a21 b 1 a22 b 2 2 3 1 5 1 1 2 2 15 3 3 0 defined For example if A 2 51 2 3 b b2 b 3 b 1 b22 23 6 a 3 b 3 a23 b 3 is another 3 Therefore addition of A and B is defined 1 2 123 01 Note 1 We emphasise that if A and B are not of the same order then A B is not 13 3 B 1 then A B is not defined 2 We may observe that addition of matrices is an example of binary operation on the set of matrices of the same order 3 4 2 Multiplication of a matrix by a scalar Now suppose that Fatima has doubled the production at a factory A in all categories refer to 3 4 1