If 
, show that A2 – 5A + 7I = O. Hence, find A – 1.
A = 
A2 = 
= 
Now, A2 – 5A + 7I = 
= 
= 
So, A2 – 5A + 7I = 0
Multiply by A – 1 both sides
= A.A. A – 1 – 5A. A – 1 + 7I. A – 1 = 0
= A – 5I + 7 A – 1 = 0
= A – 1 = 
= A – 1 = 
= A – 1 = 
19
If , show that A2 – 5A + 7I = O. Hence, find A – 1.
A =
A2 =
=
Now, A2 – 5A + 7I =
=
=
So, A2 – 5A + 7I = 0
Multiply by A – 1 both sides
= A.A. A – 1 – 5A. A – 1 + 7I. A – 1 = 0
= A – 5I + 7 A – 1 = 0
= A – 1 =
= A – 1 =
= A – 1 =