A =

|A| = x × (y × z) = xyz

Since, |A| ≠ 0

A^-1 exists

To find the inverse of a matrix we need to find the Adjoint of that matrix

For finding the adjoint of the matrix we need to find its cofactors

Let A_ij denote the cofactors of Matrix A

Minor of an element a_ij = M_{ij �}

a₁₁ = x, Minor of element a₁₁ = M₁₁ = = (y × z) – (0 × 0) = yz

a₁₂ = 0, Minor of element a₁₂ = M₁₂ = = (0 × z) – (0 × 0) = 0

a₁₃ = 0, Minor of element a₁₃ = M₁₃ = = (0 × 0) – (0 × y) = 0

a₂₁ = 0, Minor of element a₂₁ = M₂₁ = = (0 × z) – (0 × 0) = 0

a₂₂ = y, Minor of element a₂₂ = M₂₂ = = (x × z) – (0 × 0) = xz

a₂₃ = 0, Minor of element a₂₃ = M₂₃ = = (x × 0) – (0 × 0) = 0

a₃₁ = 0, Minor of element a₃₁ = M₃₁ = = (z × 0) – (0 × 0) = 0

a₃₂ = 0, Minor of element a₃₂ = M₃₂ = = (x × 0) – (0 × 0) = 0

a₃₃ = z, Minor of element a₃₃ = M₃₃ = = (x × y) – (0 × 0) = xy

Cofactor of an element a_ij, A_ij = (-1)^i+j × M_ij

A₁₁ = (-1)¹⁺¹× M₁₁ = 1 × yz = yz

A₁₂ = (-1)¹⁺²× M₁₂ = (-1) × 0 = 0

A₁₃ = (-1)¹⁺³× M₁₃ = 1 × 0 = 0

A₂₁ = (-1)²⁺¹× M₂₁ = (-1) × 0 = 0

A₂₂ = (-1)²⁺² × M₂₂ = 1 × xz = xz

A₂₃ = (-1)²⁺³ × M₂₃ = (-1) × 0 = 0

A₃₁ = (-1)³⁺¹ × M₃₁ = 1 × 0 = 0

A₃₂ = (-1)³⁺² × M₃₂ = (-1) × 0 = 0

A₃₃ = (-1)³⁺³ × M₃₃ = 1 × xy = xy

Adj A = =

A^-1 = adj A / |A|

A^-1 = /xyz

A^-1 =

A^-1 = =

The correct answer is A