Another option to keep the matrix() transformation as preserved transformation for the bitmap image would be - (in the original, externally created SVG document) - to wrap the image into a <g> element, and to apply the matrix() transformation to the group. This will then "work" in Inkscape even if the <image> has the default 'xMidYMid' value for 'preserveAspectRatio' (since the group will be transformed), and will also "survive" copy&paste into a new document, or otherwise transforming (e.g. translating aka moving) the group within the original document.
Another option to keep the matrix() transformation as preserved transformation for the bitmap image would be - (in the original, externally created SVG document) - to wrap the image into a <g> element, and to apply the matrix() transformation to the group. This will then "work" in Inkscape even if the <image> has the default 'xMidYMid' value for 'preserveAspect Ratio' (since the group will be transformed), and will also "survive" copy&paste into a new document, or otherwise transforming (e.g. translating aka moving) the group within the original document.