The inverse of symmetric matrix is??

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Answer 1 · 2018-07-30T11:32:44

Please see the explanation below.

Let the square matrix #A# be invertible

Then,

#AxxA^-1=I#

where #I# is the identity matrix.

If #A# is a symmetric matrix, then

#A=A^T#

#A^-1=(A^T)^-1#

since for all square matrices

#(M^-1)^T=(M^T)^-1#

Therefore

#A^-1=(A^-1)^T#