Can we get a Matrix from its inverse?

Question

Is there a way to get back a matrix if we know the inverse of the required matrix?

Suppose I have Y=inv(A);

How can I get A in MATLAB?

score 4 · Answer 1 · answered Sep 09 '17 at 20:05

4

By definition, the inverse of the inverse of a matrix is the matrix itself

A = inv(inv(A))

answered Sep 09 '17 at 20:05

Wolfie

3

It is not really _by definition_, but rather a property of an _invertible_ matrix: https://en.wikipedia.org/wiki/Invertible_matrix – m7913d Sep 09 '17 at 21:00

python_enthusiast · Accepted Answer · 2017-09-09T20:21:53.423

1

X = inv(Y)

If you have a matrix whose determinant is not zero,

Y*(Y^(-1)) = (Y^(-1))*Y = I

where I is the identity matrix.

edited Sep 09 '17 at 20:21

answered Sep 09 '17 at 20:05

python_enthusiast

It's perfectly ok. =) – python_enthusiast Sep 09 '17 at 20:20
3

If you have the inverse of a matrix, then by definition you must be able to invert it *again*, or you wouldn't have the inverse in the first place. Specifying the non-zero determinant condition is redundant. – Wolfie Sep 09 '17 at 20:32
Yes, I know. I added this part because you might have a right-inverse or a left-inverse of a matrix. In that case you can't do the reverse operation. But I guess the 'inv' function on matlab only works for full rank matrices, so you are right. – python_enthusiast Sep 10 '17 at 14:06

2 Answers2