Fsc Part 1 Mathematics (Complete Solution)

Q7
If A is symmetric or skew-symmetric

If A is symmetric or skew-symmetric, show that A2 is symmetric.

SOLUTION:

If A is symmetric At = A

To prove (A2)t = A2

(At)t = (A.At)t

= AtAt

= A.A

= A2

Thus A2 is symmetric At=-A

If A is skew symmetric At=-A

(A2)t = (A.A)t

= AtAt

= (-A)(-A)

= A2

Thus A2 is symmetric.

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