Question

prove that A² is symmetric if either A is symmetric or A is skew symmetric​

Answer 1

Answer:

Step-by-step explanation:

Let  B=A2  then,

Case 1:

If A=A'

=> A'A= A•A=  A2  = B (post multiplication of A)

Now,

B'= (A'A)'= AA'= (A)(A)=  A2  = B

Thus B is symmetric.

Case2:

If A'= -A

=> -A'= A

=> -A'A= A.A =  A2  = B (post multiplication of A)

Now,

B'= (-A'A)'= (-A)(A')= (-A)(-A)=  A2  = B

Thus B is symmetric.

Thus B=  A2  is symmetric even if A is symmetric or asymmetric matrix.

Hence proved.

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