How to do inverse matrix (binary from ) in matlab ?

Hello, I have this matrix in binary from

Q =

     0     0     1
     1     0     0
     0     1     0

and I wants to get the inverse matrix (binary form) in matlab? how to do it? i use this Q_inv=inv(Q) to get inverse Q

Q_inv =

     0     1     0
     0     0     1
     1     0     0

Is this Q_inv=inv(Q) is correct for inverse binary matrix ? if no, how to do it?

[Roger Stafford]

That is the true inverse of Q. If you doubt that try this:

Q*Q_inv

You will get the 3x3 identity matrix as a result. That proves that Q_inv is the correct inverse.

[z m]

Thank you.

Answer 1

[Image Analyst]

To invert values by turning 0s into 1s and 1s into 0s, use tilde:

Q = ~Q;

[Roger Stafford]

@Image Analyst: I disagree. Even on zm's example with Q, doing the negation operation does not create the multiplicative inverse. Try multiplying Q*(~Q) and you will see.

[Image Analyst]

Roger, in the image processing community, inverting a binary image means what I said. It's very very common jargon. People use it all the time.

It's not clear whether "z m" meant the inverse (or "complement") of a binary image matrix, OR the traditional matrix inverse like you'd do with any matrix. That's why I offered the alternative interpretation.

Answer 2

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/16990-galois-field-to-find-the-inverse-of-a-binary-matrix#answer_22910 for more about constructing inverses of boolean matrices.