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Calculate the inverse of : {pmatrix} 5 & 3 6 & 4 {pmatrix} .

Question

Calculate the inverse of :
$(5634)$ .

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Calculate the inverse of :

(5634)

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Text solutionVerified

Let

A = [5634]

∣ A ∣ = ∣ ∣ 5634 ∣ ∣

∴ ∣ A ∣ = 20 - 18

∴ ∣ A ∣ = 2

2) Minor matrix of A is given by,

M_{A} = [4365]

3) cofactor matrix A is given by,

C_{A} = [4 - 3 - 6 5]

4) Adjoint matrix A is given by,

A d j [A] = [C_{A}]^{T}

∴ A d j [A] = [4 - 3 - 6 5]^{T}

∴ A d j [A] = [4 - 6 - 3 5]

[A]^{- 1} = \frac{1}{∣ A ∣} A d j [A]

∴ [A]^{- 1} = \frac{1}{2} [4 - 6 - 3 5]

∴ [A]^{- 1} = [2 - 3 \frac{- 3}{2} \frac{5}{2}]

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