Abstract
In introductory linear algebra courses one continually seeks interesting sets of matrices that are closed under the operations of matrix addition, scalar multiplication, and if possible, matrix multiplication. Most texts mention symmetric and antisymmetric matrices and ask the reader to show that these sets are closed under matrix addition and scalar multiplication but fail to be closed under matrix multiplication. Few textbooks, if any, suggest an investigation of the set of matrices that are symmetric with respect to both diagonals, namely bisymmetric matrices. The following is a sequence of relatively straightforward problems that can be used as homework, class discussion, or even examination material in elementary linear algebra classes.
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