If 
show that (A2 – 5A + 7I) = O.
Given : 
Matrix A is of order 2 
2.
To show : A2 - 5A +7I = 0
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
A2 = 
= 
= 
A2 = 
5A = 5 × 
= 
5A = 
I = 
7I = 
= 
7I = 
A2 - 5A + 7I = 
+ 
= 
= 
A2 - 5A + 7I = 0
1