The inverse of symmetric matrix is??

1 Answer
Jul 30, 2018

Answer:

Please see the explanation below.

Explanation:

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#