# Addition of Matrices

The sum of two matrices is obtained by adding the corresponding elements of both the matrices. While adding two matrices, their order must be the same.

In general, if A = [aij] and B = [bij] are two matrices of same order then the sum of A and B is given by matrix C = [cij] where cij = aij + bij for all possible values of i and j.

## Properties of Matrix addition

i) Commutative Law: If A and B are any two matrices of same order then A + B = B + A

ii) Associative Law: If A, B and C are any three matrices of same order then A + (B + C) = (A + B) + C

iii) Existence of additive identity: Let A be a matrix of order m x n and 0 be an m x n zero matrix, then A + 0 = 0 + A.

iv) Existence of additive inverse: Let A be any matrix, then we can find another matrix –A such that A + (-A) = 0. So additive inverse of A is –A.

## Difference of two matrices

If A and B are two matrices of same order, then the difference A - B is obtained by subtracting the corresponding elements of A and B.

Find 2 A + B

Find A – B

3. Find the values of x and y given the following equation:

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### Reference Links:

http://en.wikipedia.org/wiki/Matrix_(mathematics)

http://en.wikipedia.org/wiki/Commutativity

http://en.wikipedia.org/wiki/Associativity