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Math Help - Hard Lin Alg.

  1. #1
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    Hard Lin Alg.

    Suppose we have two matrices, matrix A and matrix B, both of which are 5x5 matrices. Further, suppose that all the entries in A and B are nonzero. However, the third column in the PRODUCT of AB is all zero.

    1.) Can matrix A be invertible? If so, give an example. If not, justify why not.

    2.) Can matrix B be invertible? If so, give an example. If not, justify why not.

    We were given this hint:

    "Consider what the definition of the product AB of 2 matrices means"
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  2. #2
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    Quote Originally Posted by caeder012 View Post
    Suppose we have two matrices, matrix A and matrix B, both of which are 5x5 matrices.
    Further, suppose that all the entries in A and B are nonzero. However, the third column in the PRODUCT of AB is all zero.
    Can matrix A be invertible? If so, give an example. If not, justify why not.
    If A were invertible then A^{ - 1} \left( {AB} \right) = ?
    Would that matrix necessarily have zero entries?
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