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True or False? Explain. If false, show counterexample. Matrix A= a 11 a 12 a 21 a 22 , Matrix C= a 22 -a 12

True or False? Explain. If false, show counterexample.

Matrix A=

a11 a12
a21 a22

, Matrix C=

a22 -a12
-a21 a11

Call C the sister matrix of A. The sisters have opposite determinants.

Is the product of the sister matrices commutative?

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