Rules for Matrix Inversion

Question 1

(A*B)^-1

Answer 1

B^-1 * A^-1

Question 2

(A^-1)^T

Answer 2

(A^T)^-1

Question 3

Is the inverse of an invertible symmetric matrix also symmetric?

Answer 3

Yes

Question 4

When is a matrix invertible?

Answer 4

Iff it has rank n.

Iff it is square and has a non-zero determinant.