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Let A and B are n x n matrices from which A is invertible. Suppose AB is singular. What conclusion can be made about the invertibility of B?

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  1. 9 April, 05:59
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    Answer: Matrix B is non - invertible.

    Step-by-step explanation:

    A matrix is said to be be singular is its determinant is zero,

    We know that if a matrix is singular then it is not invertible. (1)

    Or if a matrix is invertible then it should be non-singular matrix. (2)

    Given : A and B are n x n matrices from which A is invertible.

    Then A must be non-singular matrix. (from 2)

    If AB is singular.

    Then either A is singular or B is singular but A is a non-singular matrix.

    Then, matrix B should be a singular matrix. (from 2)

    So Matrix B is non - invertible. (from 1)
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