In hybrid block-based video coding, transform plays an important role in energy compaction. Transform coding converts residual data in the spatial domain into frequency domain data, thereby concentrating energy in a lower frequency band. In VVC (versatile video coding), the primary transform is performed using DCT-II (discrete cosine transform type 2), DST-VII (discrete sine transform type 7), and DCT-VIII (discrete cosine transform type 8). Considering that DCT-II, DST-VII, and DCT-VIII are all linear transforms, inverse transform is proposed to reduce the number of computations by using the linearity of transform. When the proposed inverse transform using linearity is applied to the VVC encoder and decoder, run-time savings can be achieved without decreasing the coding performance relative to the VVC decoder. It is shown that, under VVC common-test conditions (CTC), average decoding time savings values of 4% and 10% are achieved for all intra (AI) and random access (RA) configurations, respectively.