Properties of Matrix Addition
If A = [ aij ] and B = [ bij ] are two matrices of the same order , say m × n . Then , the difference of the two matrices A and B is defined as a matrix C = [ cij ] m × n , where cij = aij- bij , for all possible values of i and j .
The two matrices have to be of the same order . if A and B are not of the same order , then A - B is not defined
Numerical :
Solution :
Properties of Matrix Addition
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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 .