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tiberiu_chibici_1994
tiberiu_chibici_1994 asked in Science & MathematicsMathematics · 10 years ago

Matrix multiplication at power?

A and B are matrices. Is (A * B)^n = A^n * B^n ? (n is a power)

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  • Anonymous
    10 years ago
    Favorite Answer

    this is false.

    matrix multiplication is not necessarily commutative (http://en.wikipedia.org/wiki/Commutative_property)

    i.e A*B doesn't always equal to B*A

    this property is required to state (A * B)^n = A^n * B^n

    because it states that:

    A*B*A*B*A*B*A*B..... = A*A*A*A*B*B*B*B

  • ?
    10 years ago

    NO.

    (A*B)^n = B^n * A^n

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