also
if you take the matrix A and use a sequence of row operations to reduce it to I
then those same operations applied to I will give you A inverse
since you're basically doing (P1)(P2)...(Pn)A = I
which implies (P1)(P2)...(Pn) = A^-1
an easy way to do this is to take [A|I] and reduce the left part to I
what remains on the right will be A inverse
example:
1 1
0 1
you take
1 1 1 0
0 1 0 1
then your row operations to reduce the left part into I is simply R1-R2
==>
1 0 1 -1
0 1 0 1
so the inverse is
1 -1
0 1
now you can do it for the larger matrix
"Online Matrix Calculator"
Thank you for that! Now, I'm on an old computer, so the instructions doesn't show up. But if I did it right, the inverse of the matrix should be:
-1 0 0 0
0 -1 3/2 0
0 0 1/2 0
-3/2 3/2 -3/2 1/2
Is this right?