Math Expression in bold italic

You can use the bm package for boldmath:

documentclass{article}

usepackage{bm}

begin{document}

using the inverse function $bm{x=A^{-1}y}$ 

end{document}

The boldmath command will turn math expressions following it bold, so you could write {boldmath ( x=A^{-1}y )}. Within math mode, you can use ( boldsymbol{x=A^{-1}y} ). The unicode-math and isomath packages also add a mathbfit alphabet for bold italic math letters.

To use this in LuaLaTeX or XeLaTeX, you want to load unicode-math and select a font that comes in bold, such as setmathfont{XITS Math}. You could also specify a bold math version, such as setmathfont{KpMath-Semibold.otf}[version=bold].

To use this in PDFTeX, load amsmath, and I would also recommend bm after all other math packages. However, the standard boldmath and boldsymbol commands are preferable to bm, as they are more compatible.