Let `A = [[3,a,-1],[2,5,c],[b,8,2]]` is symmetric and `B = [[d, 3, a],[b-a, e, -2b-c ],[-2, 6, -f]]` is skew- symmetric, find AB. If AB is symmetric or skew symmetric or neither of them. Justify your answer.

Let `A = [[3,a,-1],[2,5,c],[b,8,2]]` is symmetric and `B = [[d, 3, a],

1.	Let `A = [[3,a,-1],[2,5,c],[b,8,2]]` is symmetric and `B = [[d, 3, a],[b-a, e, -2b-c ],[-2, 6, -f]]` is skew- symmetric, find AB. If AB is symmetric or skew symmetric or neither of them. Justify your answer.
Answer» `because` A is symmetric `therefore c = 5, b=-1 and a =2` …(i) and B is skew- symmetrci `therefore d =e =f=0 and 2b + c = 6, a=b, b-a=-3` …(ii) From Eqs. (i) and (ii), we get `a= 2, b= -1 , c=8, d=0, e=0, f=0` `therefore A= [[3,2,-1],[2,5,8],[-1,8,2]]and B= [[0,3,2],[-3,0,-6],[-2,6,0]]` `rArr AB= [[-4,3,-6],[-31,54,-26],[-28,9, -50]]` which neither symmetric nor skew-symmetric.

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