Diagonalize the matrix A 1 1 4 1 4 1 4 1 1 Is A similar to

Diagonalize the matrix A = (1 -1 4 -1 4 -1 4 -1 1). Is A similar to B = (3 0 0 1 6 0 0 0 -3)?

Solution

Answer 2: Yes, A and B are similar matrices (As explained below)

If matrices have the same determinants, they are simlar.

So determinant for A = 1(4 - 1) + 1(-1 + 4) + 4(1 - 16) = 3 + 3 - 60 = -54

And determinant for B = 3(-18 - 0) - 1(0 - 0) + 0(0 - 0) = -54 - 0 + 0 = -54

So, A and B are similar matrices.