In other words kA k a mxn k a mx n that is i j th element of kA is ka for all possible values of i and j For example if 46 notto MATHEMATICS For example let 1 5 7 2 Example 7 If A Solution We have 3A 3 5 Negative of a matrix The negative of a matrix is denoted by A We define A 1 A 1 2 3 2 31 0 5 3 1 1 5 7 3 2 0 5 2A B 2 1 5 3 21 2 och mot 3 1 A 1 A 1 5 X Difference of matrices If A a B b are two matrices of the same order say mxn then difference A B is defined as a matrix D d where d a b for all value of i and j In other words D A B A 1 B that is sum of the matrix A and the matrix B and B then Rationalised 2023 24 3 A 5 9 3 4 5 3 5 21 9 6 0 15 1 2 3 2 3 3 1 1 0 2 4 6 462 3 then A is given by 2 3 1 1 3 H 1 1 0 2 then find 2A B A B a b a b X 2 3 4 1 6 3 1 3 4 1 6 0 2 2 5 60 5 3 4 3 Properties of matrix addition tion The addition of matrices satisfy the following properties i Commutative Law If A a B b are matrices of the same order say mx n then A B B A Now blished b a addition of numbers is commutative b a B A ii Associative Law For any three matrices A a B b C c of the same order say mx n A B C A B C