Question

For sets A and B, prove that A×B = B×A only if A =0 or B = 0 or A = B​

Answer 1

Answer:

they are equal because

Step-by-step explanation:

if A=0

then,

0×B=B×0

0=A=B

Answer 2

Answer:

Class 12

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>>Symmetric and Skew Symmetric Matrices

>>If A and B are symmetric ma...

Question



If A and B are symmetric matrices of same order, prove that AB- BA is a symmetric matrix. 

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Solution



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Given :A and B are symmetric matrices.

⇒A=A′ and B=B′

From the property of transpose of matrices. we have

AB=BA

Now consider AB−BA and by taking transpose of it, we get

(AB−BA)=(AB)−(BA)=B′A′−A′B′

Replace A′→A and B′→B

=BA−AB=−(AB−BA) (by taking negative common)

we know that a matrix is said to b skew symmetric matrix if A=−A

Hence AB−BA is skew symmetric matrices