Let A and B be two $$non-zero$$ square matrices. If the productAB is a null matrix, then

Question

Let  A  and  B      be two $$non-zero$$  square matrices. If the productAB     is a null matrix, then

Infinity Learn · Accepted Answer

Let  B      be $$non-singular$$,  then B−$$1$$     exists.  Now,  $$AB=O$$      (given)⇒         (AB)B$$−$$1=OB$$−$$1$$                            $$(post-multiplying$$ both  sides by B−$$1$$     $$)⇒    $$A(BB$$−$$1)=O$$           (by$$  $$associativity)⇒    $$AIn=O$$                  $$($$∵  BB−$$1=In)$$     ⇒   $$A=O$$     But  A is $$non-null$$ matrix. Hence,  b is a singular matrix.Similarly,  it can be shown that A is a singular matrix.

Let $A a n d B$ be two non-zero square matrices. If the product $A B$ is a null matrix, then

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Let A and B be two non-zero square matrices. If the productAB is a null matrix, then

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Let $A a n d B$ be two non-zero square matrices. If the product $A B$ is a null matrix, then