If and are two square matrices of the same order such that then prove that A and B commute i.e. AB=BA
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Originally Posted by pankaj If and are two square matrices of the same order such that then prove that A and B commute i.e. AB=BA If then (I is the identity matrix). So is the inverse of and therefore commutes with it. Thus , from which .
So if does it always mean that and are inverse of each other.What if any one of or is singular matrix
Originally Posted by pankaj So if does it always mean that and are inverse of each other.What if any one of or is singular matrix If then C and D cannot be singular. One way to see this is to notice that the determinant is multiplicative: , so that and cannot be 0.
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