As of Blender 4.0, if you are trying to find the inverses of transformations made outside of Geometry Nodes, then you can use the following nodes below.
Inverse Translation. To invert your position, you can multiply each scalar of your position/vector by -1 with the Multiply operation of the
Vector Math node. Alternatively, you can use the Scale operation with value -1 to invert your entire vector. The later seems to be what most people prefer to use.
Inverse Rotation. Since Blender 4.0 has added the Quaternion data type and new nodes associated with this data type, you can invert your rotation by using the new
Invert Rotation Node. Supposedly, Blender 4.1 has already integrated the conversions between Quaternions and all existing data types. But, as of submitting this answer, you would still need to use the conversion nodes,
Euler to Rotation and
Rotation to Euler with the
Invert Rotation Node.
Note. You can easily zero the rotation by aligning your object's axis' to the world origin as Robin Betts mentioned. However, since you are asking for the Inverse Transformation to apply to another object, I gave you the actual transformation instead. Also, to note, if you're still using previous versions of Blender, then Robin Betts answer would be more suitable for your needs.
Inverse Scale. To invert your scale, simply take 1 and divide by your Scale vector. Since a single value n, is converted to vector (n,n,n), when connected, I used a single value node with the Divide operation of the
Vector Math node.
The above Inverse Transformations work great independently. However, as noticed by Markus von Broady, if you're trying to invert two or more outside transformations then the order of transformations needs to be reversed as well.
Order of Transformations. Blender applies transformations in the following order, Scale, Rotation, and finally Translation. To reverse the transformations, simply separate the transformations and apply them in reverse order.
Note. DO NOT ATTEMPT to invert a negative scale value along with another transformation. The Inverted Transforms fails because the object info node only outputs positive scale values.
I could not find a work around for this as it seems to be an issue with Geometry Nodes itself. You can invert the scale with negative values independently but just not along with the other inverted transformations.
I created a custom node group called "Invert Transform Geometry" with your desired Invert checkbox in the file below for you.
Hope this helps.