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prove that if a is not equal to zero and if a * b = a * c and a ^ b = a ^ c then b = c [Hint: calculate a * (b-c) and a ^ (b-c) vectors mechanics

  • maths -

    a*b = a*c
    a*b - a*c = 0
    a*(b-c) = 0
    if a≠0, b-c = 0, since the product is zero.
    b-c = 0
    b = c

    a^b = a^c
    a^b / a^c = 1
    a^(b-c) = a^0
    b-c = 0
    b = c

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