So
– A is the additive inverse of A or negative of A 3 4 4  Properties of scalar multiplication of a matrix
If A = [aij] and B = [bij] be two matrices of the same order, say m × n, and k and l are
scalars, then
(i)
k(A +B) = k A + kB, (ii) (k + l)A = k A + l A
(ii)
k (A + B) = k ([aij] + [bij])
= k [aij + bij] = [k (aij + bij)] = [(k aij) + (k bij)]
= [k aij] + [k bij] = k [aij] + k [bij] = kA + kB
(iii)
( k + l) A = (k + l) [aij]
= [(k + l) aij] + [k aij] + [l aij] = k [aij] + l [aij] = k A + l A
Example 8 If 
8
0
2
2
A
4
2 and B
4
2
3
6
5 1
−








=
−
=








−




, then find the matrix X, such that
2A + 3X = 5B