Verify that A(B + C) = (AB + AC), when
and 
Given : 
and 
Matrix A is of order 2 
2 , matrix B is of order 2 
2 and matrix C is of order 2 
2
To verify : A(B + C) = (AB + AC)
Formula used :
Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj
If A is a matrix of order a 
b and B is a matrix of order c 
d ,then matrix AB exists and is of order a 
d ,if and only if b = c
If A is a matrix of order a 
b and B is a matrix of order c 
d ,then matrix BA exists and is of order c 
b ,if and only if d = a
B + C = 
+ 
= 
= 
B + C = 
Matrix A(B + C) is of order 2 x 2
A(B + C) = 
= 
A(B + C) = 
= 
A(B + C) = 
For matrix AB, a = b = c = d = 2 ,matrix AB is of order 2 x 2
Matrix AB = 
= 
Matrix AB = 
= 
Matrix AB = 
For matrix AC, a = b = c = d = 2 ,matrix AC is of order 2 x 2
Matrix AC = 
= 
Matrix AC = 
= 
Matrix AC = 
Matrix AB + AC = 
+ 
= 
= 
Matrix AB + AC = A(B + C) = 
A(B + C) = (AB + AC)