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