Inverse of a Matrix

Worked Solution:

The inverse M^-1 of a matrix M (if it has one) is the matrix that makes their product equal to the Identity matrix:

M-1 M = M M-1 =

( 1 0 0 1 )

For M =

( a b c d )

the product

( a b c d )

( d –b –c a )

is

( a d – b c 0 0 a d – b c )

If we divide the elements of the second matrix by a d – b c
which for the matrix in this question is (–1)×(–1) – 4×6 = –23
the product will be the Identity Matrix:

So the inverse of

( –1 4 6 –1 )

is

–  1 23

( –1 –4 –6 –1 )

=

( 1 23 4 23 6 23 1 23 )