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प्रश्न
Answer the following question:
If A = `[(3, -5),(-4, 2)]`, show that A2 – 5A – 14I = 0
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उत्तर
A2 – 5A – 14I
= A.A – 5A – 14I
= `[(3, -5),(-4, 2)] [(3, -5),(-4, 2)] -5[(3, -5),(-4, 2)] -14[(1, 0),(0, 1)]`
= `[(9 + 20, -15 - 10),(-12 - 8, 20 + 4)] - [(15, -25),(-20, 10)] - [(14, 0),(0, 14)]`
= `[(29, -25),(-20, 24)] - [(15, -25),(-20, 10)] - [(14, 0),(0, 14)]`
= `[(29 - 15 - 14, -25 + 25 - 0),(-20 + 20 - 0, 24 - 10 - 14)]`
= `[(0, 0),(0, 0)]`
= 0
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