Show that satisfies the equation A² + 4A – 42I = O. Hence, find A ^{– 1}.

A =

A² = =

=

4A = 4

42I = 42

Now,

A² + 4A – 42I =

=

Hence, =

Now, A² + 4A – 42I = 0

= A ^{– 1}. A . A + 4 A ^{– 1}.A – 42 A ^{– 1}.I = 0

= IA + 4I – 42A ^{– 1} = 0

= 42A ^{– 1 =} A + 4I

= A ^{– 1 =}

=

A ^{– 1 =}