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प्रश्न
If A = `[(3, 4),(-4, 3)] and "B" = [(2, 1),(-1, 2)]`, show that (A + B)(A – B) = A2 – B2
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उत्तर
We have to prove that (A + B)(A – B) = A2 – B2,
i.e., to prove A2 – AB + BA – B2 = A2 – B2,
i.e., to prove – AB + BA = 0,
i.e., to prove AB = BA.
AB = `[(3, 4),(-4, 3)] [(2, 1),(-1, 2)]`
= `[(6 - 4, 3 + 8),(- 8 - 3, -4 + 6)]`
= `[(2, 11),(-11, 2)]` ...(i)
BA = `[(2, 1),(-1, 2)] [(3, 4),(-4, 3)]`
= `[(6 - 4, 8 + 3),(-3 - 8, -4 + 6)]`
= `[(2, 11),(-11, 2)]` ...(ii)
From (i) and (ii), we get
AB = BA
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