ALGEBRA OF MATRICES
Addition and Subtraction of Matrices:
Any two matrices can be added if they are of the same order and the resulting matrix is of the same order. If two matrices A and B are of the same order, they are said to be conformable for addition.
All the laws of ordinary algebra hold for the addition or subtraction of matrices and their multiplication by scalars.
(i). If A and B be two matrices of the same order and if k be a scalar, then
k(A + B) = kA + kB
(ii). If k1 and k2 are two scalars and if A is a matrix, then
(k1 + k2)A = k1A + k2A and k1(k2A) = k2(k1A)
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