A={{1,2,3,4,5},{2,5,3,4,1},{0,-2,4,3,7}}

RowReduce[A]

%//MatrixForm

A={{1,2,3},{4,5,6},{7,8,9}}

B=DiagonalMatrix[{2,5,3}]

A^2  . Transpose[B]//MatrixForm

Det[A]

A={{1.0,2,3},{4,5,6},{7,8,9}}

Eigenvalues[A]

Eigenvectors[A]

A={{1,2,3},{4,5,6},{7,8,9}}

JordanDecomposition[A]