Show that the matrix is nonsingular if and only if ad-bc≠0. If this condition holds, show that

I think what I want to do is show that is row equivalent to . When I was doing this I got stuck at

- Feb 5th 2011, 02:40 PMJskidshow that the matrix is non singular if and only if this condition is met
Show that the matrix is nonsingular if and only if ad-bc≠0. If this condition holds, show that

I think what I want to do is show that is row equivalent to . When I was doing this I got stuck at - Feb 5th 2011, 08:48 PMTinyboss
Showing that the inverse is given by that particular matrix (with ad-bc in the denominators) gives you one direction. To do the other, suppose ad-bc=0 and try multiplying the top row by d and the bottom row by b.

- Feb 6th 2011, 05:51 AMHallsofIvy
Show that .

Since the inverse of a matrix is unique, it follows that the denominator of that fraction cannot be 0.