Class 12 Maths Matrices Properties of Matrix Addition

Properties of Matrix Addition

  • Commutative Law
  • Associative Law
  • Existence of additive identity
  • The existence of additive inverse

 

Commutative Law : If A = [aij], B = [bij] are matrices of the same order, say m × n, then A + B = B + A.

Associative Law : For any three matrices A = [aij], B = [bij], C = [cij] of the same order, say m × n, (A + B) + C = A + (B + C).

Existence of additive identity : Let A = [aij] be an m × n matrix and O be an m × n zero matrix, then A + O = O + A = A. In other words, O is the additive identity for matrix addition.

 

The existence of additive inverse :  Let A = [aij]m × n be any matrix, then we have another matrix as – A = [– aij]m × n such that A + (– A) = (– A) + A= O. So – A is the additive inverse of A or negative of A.

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