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Orthogonal matrix whose submatrix has special properties

  1. Oct 20, 2009 #1
    Dear Forumers.

    I am working on the following problem.

    Let matrix P=( A B ) where A and B are matrices. Let P be an n*n orthogonal matrix.

    Show that A'A is an idempotent matrix.

    I do not know where to start. Thanks in advance for the help.
  2. jcsd
  3. Oct 20, 2009 #2
    I can write
    PP'=(A B)(A B)'
    =(AB'+AA' BB' +BA')

    and I can write
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