Poolelinalg4 3.2.036.(a)give an example to show that if a and b are symmetricn ✕ nmatrices, then ab need not be symmetric. a =0 22 0, b =0 11 0; but ab =2 00 2which is not symmetrica =1 11 0, b =0 11 0; but ab =1 10 1which is not symmetrica =1 21 0, b =0 11 0; but ab =2 10 1which is not symmetrica =1 01 0, b =0 11 0; but ab =0 10 1which is not symmetrica =1 21 0, b =0 12 0; but ab =4 10 1which is not symmetric(b)prove that if a and b are symmetricn ✕ nmatrices, then ab is symmetric if and only ifab = ba. suppose a and b are symmetric. then (ab)t = btat = ba. thus, ab is symmetric if and only if ab = (ab)t = ba. suppose a and b are symmetric. then (ab)t = atbt = −ab. thus, ab is symmetric if and only if −ba = (ab)t = ab. suppose a and b are symmetric. then (ab)t = ab and (ba)t = ba. thus, ab is symmetric if and only if ab = (ab)t = (ba)t = ba. suppose a and b are symmetric. then (ab)t = btat = −ba. thus, ab is symmetric if and only if −ab = (ab)t = ba. suppose a and b are symmetric. then (ab)t = atbt = ab. thus, ab is symmetric if and only if ba = (ab)t = ab. need ? read it talk to a tutor