Addition of matrices: If two matrices A and B are of the same order mxn, then the sum A+B is of the same order mxn and contains the elements obtained by adding the corresponding elements of A and B.
Scalar multiplication: If A is a matrix of order mxn and ‘k’ is a scalar then kA is a matrix of same order mxn whose elements are the products of k with the corresponding elements of A.
Here, -A = (-1) A and so A-B = A+(-B)
Properties of matrix addition and multiplication:
a) Associative law:
A+(B+C) = (A+B)+C
b) Commutative law:
A + B = B + A.
c) k(A+B) = kA + kB, where k is a scalar.
d) Law of identity:
If A is a matrix of order mxn and O is a null matrix of same order then
A+O = O+A = A, where O is called the additive identity.
e) Law of inverse:
If A is a matrix of order mxn then the additive inverse of A which is –A is also of same order and A+(-A) = (-A)+A =O