A cytoskeleton is present in all cells of all domains of life (archaea, bacteria, eukaryotes). It is a complex network of interlinking filaments and tubules that extend throughout the cytoplasm, from the nucleus to the plasma membrane. The cytoskeletal systems of different organisms are composed of similar proteins. In eukaryotes, the cytoskeletal matrix is a dynamic structure composed of three main proteins, which are capable of rapid growth or disassembly dependent on the cell's requirements at a certain period of time.

Is it true that do both plant and animal cells have a cytoskeleton?
yes