# Linear Algebra Question: Matrices and Symmetry

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Assume that A and B are two symmetric k x k matrices.

a) Show that AB = (BA)^T

b) Show that if A is invertible, then A^-1 is also a symmetric matrix.

c) Assume that we can write

A= [ A_1 A_2 ]

A_3 A_4

With A_1 a 2 x 2, A_2 an m x 3, A_3 a 3 x n and A_4 a p x q matrix. What can we say about m, n, p, q? Which of the four submatrices is symmetric? Can you say anything about the relationship between A_2 and A_3?

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