If , find A–1 and prove that A2 – 4A–5I = O.
A =
A2 =
=
A2 – 4A + 5I = 0
Also, A2 – 4A – 5I = 0
Now, 6(A.A) A – 1 – 4.A A – 1 – 5I.A – 1 = 0
= A – 4I – 5A – 1 = 0
= A – 1 =
Hence, A – 1 =