SOME BASIC PROPERTIES OF MATRICES...
1)Let A & B be the 2 matrices of same order...then (A+B)' = A' + B'
2)Let A and B be two matrices , such that AB is defined , then B'A' is also defined(AB)' = B'A'
3)Let A , A & Cbe the matrices of same order , then A + B = B + A and (A+B) + C = A+ (B+C)
4)Let A , B & C are the matrices of orders m x n , n x p , p x q , resp. (so that both AB and BC are defined ) , then
(AB)C = A(BC)
5)Cancellation law hold good in caseof addition of matrices of same order then
A + B = A + C => B = C
B + A = C + A => B = C
6)If A & B are 2 matrices of the same order an k is scalar , then k (A + B ) = kA + kB
7)If k1 & k2 are 2 scalarsand A is any matrix , then (k1 + k2)A = k1A + k2A
8)If k1 and k2 are 2 scalars and if A is a matrix , then (k1k2)A = k1(k2A) = k2 (k1A)
9)If A is a sq. matrix of order n , then A2 is defined as AA , in general , Am = AAA---------A (m tyms)
10)Let A and B be the 2 matrices , such tha AB is defined , then it is nt essential that BA is also defined , and if BA is also defined , then its nt necessary that BA = AB
11)Let A b matrix of order m x n and O be the zero matrix of order n x p then A.O= O but if A & B are 2 non zero matrices such that AB is defined , then AB still can b = to 0. i.e AB = O does not imply that either A = O or B = O
SELF WRITTEN , HOPE THIS HELPS....
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