Show that the matrix, 
satisfies the equation, A3 – A2 – 3A – I3 = O. Hence, find A–1.
A = 
A3 = A2.A
A2 = 
= 
A2.A = 
= 
= 
Now, A3 – A2 – 3A – I
= 
= 
= 
Thus, A3 – A2 – 3A – I
Now, (AAA) A – 1. – (A.A) A – 1 – 3.A A – 1 – I.A – 1 = 0
AA(A – 1A) – A(A – 1A) – 3(A – 1A) = – 1(A – 1I)
A2 – A – 3A – I = 0
= A – 1 = 
Now,
= 
= 
= 
Hence, A – 1 = 
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