If A = [8-4-53], verify that A(adj A) = (adj A)A = |A|I2 - Mathematics

If A = `[(8, -4),(-5, 3)]`, verify that A(adj A) = (adj A)A = |A|I₂

Sum

A = `[(8, -4),(-5, 3)]`

|A| = 24 – 20 = 4 ≠ 0.A^–1 ecists.

adj A = `[(3, 4),(5, 8)]`

A(adj A) = `[(8, -4),(-5, 3)][(3, 4),(5, 8)]`

= `[(24 - 20, 32 - 32),(-15 + 15, -20 + 24)]`

= `[(4, 0),(0, 4)]` ........(1)

(adj A)A = `[(3, 4),(5, 8)][(8, -4),(-5, 3)]`

= `[(24 - 20, -12 + 12),(-40 + 40, -20 + 24)]`

= `[(4, 0),(0, 4)]` ........(2)

|A|I₂ = `4[(1, 0),(0, 1)]`

= `[(4, 0),(0, 4)]` ........(3)

(1), (2) and (3)

⇒ A(adj A) = (adj A)A = |A|I₂

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Inverse of a Non-singular Square Matrix

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Chapter 1: Applications of Matrices and Determinants - Exercise 1.1 [Page 16]

Chapter 1 Applications of Matrices and Determinants
Exercise 1.1 | Q 6 | Page 16

Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`

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