CLASS-10
SOME IMPORTANT PROPERTIES OF MATRICES

Some Important Properties of Matrices –

Let,  A, B, and C be any matrices, each of order (2 X 2). Then, we have –

(i)    Commutative Law of Addition :- (A + B) = (B + A)

(ii)   Associative Law of Addition :- (A + B) + C = A + (B + C)

(iii)   A + 0 = 0 + A = A, where 0 is a (2 X 2) zero matrix

(iv)    A + (- A) =  (- A) + A = 0

(v)     X + A  =  B  =>   (X + A) + (- A) = B + (-A)

                        =>   X + [A + (- A)] = B – A

                        =>   X + 0  =  B – A

                        =>   X  =  B - A

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