CBSE Class 12 Maths Notes: Matrices – Algebra of Matrices

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.

Properties:

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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