Give an example of two non zero 2x2 matrices A and B such that AB=0.

Asked by lekhakarthikeyan | 27th Dec, 2018, 02:28: AM

Expert Answer:

begin mathsize 16px style Consider comma space straight A equals open square brackets table row 1 cell negative 1 end cell row 3 cell negative 3 end cell end table close square brackets space and space straight B equals open square brackets table row 1 2 row 1 2 end table close square brackets
AB equals open square brackets table row 1 cell negative 1 end cell row 3 cell negative 3 end cell end table close square brackets space open square brackets table row 1 2 row 1 2 end table close square brackets
AB equals open square brackets table row cell 1 cross times 1 plus open parentheses negative 1 close parentheses cross times 1 end cell cell 1 cross times 2 plus open parentheses negative 1 close parentheses cross times 2 end cell row cell 3 cross times 1 plus open parentheses negative 3 close parentheses cross times 1 end cell cell 3 cross times 2 plus open parentheses negative 3 close parentheses cross times 2 end cell end table close square brackets space
AB equals open square brackets table row 0 0 row 0 0 end table close square brackets space equals straight O end style

Answered by Sneha shidid | 27th Dec, 2018, 10:25: AM