Gaussian elimination

M(M^-1)=I
Solve for M^-1
the augmented matrix for guassian elimination=
{1 2 1 l 1 0 0}
{1 -1 1 l 0 1 0}
{3 0 2 l 0 0 1}

R2-R1 --> R2
R3-3R1 --> R3

{1 2 1 l 1 0 0}
{0 -3 0 l -1 1 0}
{0 -6 -1 l -3 0 1}

R2 / -3 --> R2
R3 / -6 --> R3

{1 2 1 l 1 0 0 }
{0 1 0 l 1/3 -1/3 0 }
{0 1 1/6 l 1/2 0 -1/6}

R1-2R2 --> R1
R3-R2 --> R3

{1 0 1 l 1/3 2/3 0 }
{0 1 0 l 1/3 -1/3 0 }
{0 0 1/6 l 1/6 1/3 -1/6}

R1-6R3 --> R1
6R3 --> R3

{1 0 0 l -2/3 -4/3 1 }
{0 1 0 l 1/3 -1/3 0 }
{0 0 1 l 1 2 -1}


M^-1 =
{ -2/3 -4/3 1 }
{ 1/3 -1/3 0 }
{ 1 2 -1}