# Tricky matrix inverse

Suppose A is a invertible n-by-n matrix. Let B be the inverse of A, i.e. B = A^(-1).It is trivial that A = B^(-1).

If we construct a matrix C whose entry is the square of corresponding entry of B, i.e. C_ij = (B_ij)^2, then we compute the inverse of C.

We can compute the inverse of C directly from A without going through the inverse operation twice?

Thank you!

## Answers and Replies

AlephZero
Homework Helper
C is not necessarily invertible, so the answer to your question is "no".

For example
$$B = \begin{matrix} 1 & -1 \cr 1 & 1 \end{matrix}$$

$$C = \begin{matrix} 1 & 1 \cr 1 & 1 \end{matrix}$$

What if we only consider A is positive definite? Then B is positive definite and C should be positive definite too.

Can we compute the inverse of C directly from A in this case?

Thank you!

AlephZero