Singular matrix or ill$-$conditioned matrix

$[$ Choose $]$Element$-$by$-$element array power operator$2$D numeric array used in linear algebra with special mathematical properties$$Matrix multiplication operator$$Result is orthogonal to the plane defined by the two input vectors$$A matrix for which an inverse does not exist$$A matrix for which an inverse does exist$$Interchanges the rows and columns$$Matrix power operator$$Container for multiple pieces of orderly information$$Element$-$by$-$element array multiplication operator$$