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Find the adjoint of each of the following Matrices.

Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)

For the matrix A= , show that A(adj A)=O.

If , show that adj A=A.

If , show that adj A=3A^{T}.

Find A (adj A) for the matrix A=.

Find the inverse of each of the following matrices:

Find the inverse of each of the following matrices.

Find the inverse of each of the following matrices and verify that A ^{– 1} A = I_{3}.

For the following pairs of matrices verify that (AB)^{–1} = B ^{– 1}A ^{– 1}:

A=

Let . Find (AB) ^{– 1}.

Given , compute A ^{– 1} and show that 2A ^{– 1} = 9I – A.

If , then show that A – 3I = 2 (I + 3A ^{– 1}).

Find the inverse of the matrix and show that aA ^{– 1} = (a^{2} + bc + 1) I – aA.

Given . Compute (AB) ^{– 1}.

Let and . Show that

[F (α)] ^{– 1} = F( – α)

[G(β)] ^{– 1} = G( – β)

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

If , verify that A^{2} – 4 A + I = O, where and . Hence, find A ^{– 1}.

Show that satisfies the equation A^{2} + 4A – 42I = O. Hence, find A ^{– 1}.

If , show that A^{2} – 5A + 7I = O. Hence, find A ^{– 1}.

If A = find x and y such A^{2} – xA + yI = O. Hence, evaluate A ^{– 1}.

If , find the value of λ so that A^{2} = λA – 2I. Hence, find A ^{– 1}.

Show that satisfies the equation x^{2} – 3A – 7 = 0. Thus, find A ^{– 1}.

Show that satisfies the equation x^{2}–12 x + 1 = 0. Thus, find A ^{– 1}

For the matrix . Show that A^{3} – 6A^{2} + 5A + 11I_{3} = O.Hence, find A ^{– 1}.

Show that the matrix, satisfies the equation, A^{3} – A^{2} – 3A – I_{3} = O. Hence, find A^{–1}.

If . Verify that A^{3} – 6A^{2} + 9A – 4I = O and hence fid A ^{– 1}.

If , prove that A ^{– 1} = A^{T}.

If , show that A ^{– 1} = A^{3}.

If , Show that A^{2} = A^{–1}.

Solve the matrix equation , where X is a 2x2 matrix.

Find the matrix X satisfying the matrix equation: .

Find the matrix X for which: .

Find the matrix X satisfying the equation: .

If , find A^{–1} and prove that A^{2} – 4A–5I = O.

If A is a square matrix of order n, prove that |A adj A| = |A|^{n}.

If A ^{– 1} = and , find (AB) ^{– 1}.

If , find (A^{T}) ^{– 1}.

Find the adjoint of the matrix and hence show that A(adj A) = |A| I_{3}.

If , find A ^{– 1} and show that A ^{– 1} = 1/2(A^{2} – 3I).

Find the inverse of each of the following matrices by using elementary row transformations: