2. Let A be a 3 x 3 matrix such that det(A)= -4. Find det(3A)

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2. Let A be a 3 x 3 matrix such that det(A)= -4. Find det(3A)

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Skylar 2 weeks 2021-09-09T12:29:49+00:00 1 Answer 0

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    2021-09-09T12:31:41+00:00

    Answer:

    The value of det (3A) is -108.

    Step-by-step explanation:

    If M is square matrix of order n x n, then

    |kA|=k^n|A|

    Let as consider a matrix A or order 3 x 3. Using the above mentioned property of determinant we get

    |kA|=k^3|A|

    We need to find the value of det(3A).

    |3A|=3^3|A|

    |3A|=27|A|

    It is given that the det(A)= -4. Substitute |A|=-4 in the above equation.

    |3A|=27(-4)

    |3A|=-108

    Therefore the value of det (3A) is -108.

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