Changing a matrix from right-handed to left-handed coordinate system

Question

I would like to change a 4x4 matrix from a right handed system where:
x is left and right, y is front and back and z is up and down

to a left-handed system where

Answer 1

Since this seems like a homework answer; i'll give you a start at a hint: What can you do to make the determinant of the matrix negative?

Further (better hint): Since you already know how to do that transformation with individual vectors, don't you think you'd be able to do it with the basis vectors that span the transformation the matrix represents? (Remember that a matrix can be viewed as a linear transormation performed on a tuple of unit vectors)