DD={{0,1,0,0},{0,0,1,1},{0,1,1,0},{1,0,0,1}}

Det[DD]

Inverse[DD]

DD . Inverse[DD] ==IdentityMatrix[4]

A={{2,1},{1,2}}

A - l*IdentityMatrix[2]

Det[Out[11]]

Solve[Out[13]==0]

Eigenvalues[A]

Eigenvectors[A]

EV1 =Out[17][[1]]

EV2 = Out[17][[2]]

A.EV2 == EV2*1

Transpose[A] == A