void MyGraphicsItem::flipHorizontal()
{
    // Get the current transform
    QTransform transform(this->transform());
 
    qreal m11 = transform.m11();    // Horizontal scaling
    qreal m12 = transform.m12();    // Vertical shearing
    qreal m13 = transform.m13();    // Horizontal Projection
    qreal m21 = transform.m21();    // Horizontal shearing
    qreal m22 = transform.m22();    // vertical scaling
    qreal m23 = transform.m23();    // Vertical Projection
    qreal m31 = transform.m31();    // Horizontal Position (DX)
    qreal m32 = transform.m32();    // Vertical Position (DY)
    qreal m33 = transform.m33();    // Addtional Projection Factor
 
    // We need this in a minute
    qreal scale = m11;
 
    // Horizontal flip
    m11 = -m11;
 
    // Re-position back to origin
    if(m31 > 0)
        m31 = 0;
    else
        m31 = (boundingRect().width() * scale);
 
    // Write back to the matrix
    transform.setMatrix(m11, m12, m13, m21, m22, m23, m31, m32, m33);
 
    // Set the items transformation
    setTransform(transform);
}
 
void MyGraphicsItem::flipVertical()
{
    // Get the current transform
    QTransform transform(this->transform());
 
    qreal m11 = transform.m11();    // Horizontal scaling
    qreal m12 = transform.m12();    // Vertical shearing
    qreal m13 = transform.m13();    // Horizontal Projection
    qreal m21 = transform.m21();    // Horizontal shearing
    qreal m22 = transform.m22();    // vertical scaling
    qreal m23 = transform.m23();    // Vertical Projection
    qreal m31 = transform.m31();    // Horizontal Position (DX)
    qreal m32 = transform.m32();    // Vertical Position (DY)
    qreal m33 = transform.m33();    // Addtional Projection Factor
 
    // We need this in a minute
    qreal scale = m22;
 
    // Vertical flip
    m22 = -m22;
 
    // Re-position back to origin
    if(m32 > 0)
        m32 = 0;
    else
        m32 = (boundingRect().height() * scale);
 
    // Write back to the matrix
    transform.setMatrix(m11, m12, m13, m21, m22, m23, m31, m32, m33);
 
    // Set the items transformation
    setTransform(transform);
}

void dump_transform(QTransform& t, const char* name)
{
    qreal _m11 = t.m11();    // Horizontal scaling
    qreal _m12 = t.m12();    // Vertical shearing
    qreal _m13 = t.m13();    // Horizontal Projection
    qreal _m21 = t.m21();    // Horizontal shearing
    qreal _m22 = t.m22();    // vertical scaling
    qreal _m23 = t.m23();    // Vertical Projection
    qreal _m31 = t.m31();    // Horizontal Position (DX)
    qreal _m32 = t.m32();    // Vertical Position (DY)
    qreal _m33 = t.m33();    // Addtional Projection Factor

    qDebug("================ %s ==================", name);
    qDebug("m11: %f, m12: %f, m13: %f", _m11, _m12, _m13);
    qDebug("m21: %f, m22: %f, m23: %f", _m21, _m22, _m23);
    qDebug("m31: %f, m32: %f, m33: %f", _m31, _m32, _m33);
}

• https://gerrysweeney.com/horizontal-and-vertical-flip-transformations-of-a-qgraphicsitem-in-qt-qgraphicsview/