Homework Help: Anyone can prove this ?

1. Jan 24, 2010

ahmed dawod

1. show that if a square matrix A satisfies A^3+4A^2 -2A+7i=0 then so does A^T

i is the identity matrix

3. The attempt at a solution

I tried to multiply the equation by A^T but all in vain

2. Jan 24, 2010

rasmhop

Use:
$$(A+B)^T = A^T + B^T \qquad (AB)^T = A^TB^T \qquad (cA)^T = cA^T$$
to compute the transpose by using:
$$0 = 0^T = (A^3 + 4A^2 - 2A + 7I)^T$$

3. Jan 24, 2010

ahmed dawod

thanks
this is useful

problem solved