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

MatrixForm[A]

b=(({{2}, {1}, {4}}))

x=LinearSolve[A,b]

A.x==b

A1=(({{1, -2, 2, 2}, {3, -4, 1, 1}, {-2, 3, 5, 4}}))

RowReduce[A1]//MatrixForm

A2={{1,3,-2},{-2,-4,3a},{2,1,5a}}

b2=(({{2}, {1}, {4}}))
x=LinearSolve[A2,b2]

c={{2,-3},{-1,4}}//MatrixForm

Det[A-λ*IdentityMatrix[3]]

CharacteristicPolynomial[A,λ]

Eigenvalues[A]

Eigenvectors[A]