A matrix A is symmetric if A AT middot If A is nonsingular

A matrix A is symmetric if A = A^T middot If A is non-singular, is A^-1 symmetric? Yes No Answer: NOTES:

Solution

A non-singular matrix A is invertible. It does not have to be necessarily symmetric. Foor example, a 3 x 3 matrix A with (1,2,3), (2,3,4) and (4,5,6) as its 1st, 2nd and 3rd rows is not symmetic, but it is non singular and its inverse A^-1has ( -5,5, -1), (6,-7,2) and (-2,3,-1) as its 1st, 2nd and 3rd rows. The statement is False.