Q16 of 74 Page 7

Let and . Show that
[F (α)] ^{– 1} = F( – α)

F(α) =

| F(α)| = = 1

Cofactors of A are:

C₁₁ = cos α C₂₁ = sin α C₃₁ = 0

C₁₂ = – sin α C₂₂ = cos α C₃₂ = 0

C₁₃ = 0 C₂₃ = – 10 C₃₃ = 1

adj F(α) =

So, adj F(α) = …… (i)

Now, [F(α)] ^{– 1} =

And, F( – α) = …… (ii)

Hence, [F (α)] ^{– 1} = F( – α)

Find the inverse of the matrix and show that aA ^{– 1} = (a² + bc + 1) I – aA.

Given . Compute (AB) ^{– 1}.

Let and . Show that

[G(β)] ^{– 1} = G( – β)

Let and . Show that

[F(α)G(β)] ^{– 1} = G – ( – β) F( – α).

Let and . Show that[F (α)] – 1 = F( – α)