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If AB=> BA, for two square matrices, A and B, we say that A and B commute. One interesting case is diagonal matrices, which always commute.

The adjoint (or transpose) of the product of two matrices is equal to the product of the adjoints (or transposes) of the two matrices taken in the opposite order:

{AB)T-BTAT

This result easily generalizes to products of more than two matrices.

Multiplying any matrix by the identity matrix of the appropriate order, on the left or the right, yields a product equal to the original matrix. Thus, if B is of order

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