if A and B are n* n matrix, and AB is not equal to BA . and ABA is equal to A^2B; BAB is equal to B^2 A; then prove that A+B is not invertible.

Printable View

- Aug 24th 2007, 10:12 AMkamaksh_icematrix products
if A and B are n* n matrix, and AB is not equal to BA . and ABA is equal to A^2B; BAB is equal to B^2 A; then prove that A+B is not invertible.

- Aug 24th 2007, 11:33 AMred_dog
I think is not true.

Let such that and . Then .

But and and there are not equal. - Aug 24th 2007, 11:38 AMSoroban
Hello, kamaksh_ice!

Is there a typo in the problem?

. . The statement is not true . . .

Quote:

If and are matrices, and ,

. . prove that: .

Let: .

. .

. .

Ha! red_dog beat me to it ... and explained it better!

.