{a,b,c}

m={{a,b},{c,d}}

m// MatrixForm

m[[1]]

m[[1,2]]

v={x,y}

p v+q

v+{xp,yp}+{xpp,ypp}

{x,y}.{xp,yp}

{x,y}{xp,yp}

m.v

v.m

m.m //MatrixForm

v.m.v

Dot[v,m,v]

Det[m]

Transpose[m]// MatrixForm

n=Inverse[m]

n . m //Simplify

m . n //Simplify

h3=Table[1/(i+j-1),{i,3},{j,3}]
Det[h3]

Inverse[h3]//MatrixForm

h4=Table[1/(i+j-1),{i,4},{j,4}]
Det[h4]

Inverse[h4]//MatrixForm

h3.Inverse[h3]
h4.Inverse[h4]

r=Table[i+j+1,{i,3},{j,3}]
Eigenvalues[r]
Eigenvectors[r]

rn=N[r]
Eigenvalues[rn]
Eigenvectors[rn]

mm=Array[a,{3,3}]

Minors[mm,2]

tr=Sum[m[[i,i]],{i,2}]

Tr[m]

MatrixPower[m,3]

m^3

mmm=(({{0.4, 0.6}, {0.525, 0.475}}))

MatrixPower[mmm,3]

mmm.mmm.mmm

MatrixExp[mmm]

Exp[mmm]