`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, then find AB.

Explanation

`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.