Question

The sum of two idempotent matrices A and B is idempotent if

• A. AB = BA = 1
• B. AB = BA = O
• C. AB = BA = A
• D. AB = BA = B.

Answer 1

Answer: (B)

Since A, B are idempotent
$\therefore$ $A^2=A;B^2=B$
Now $(A+B{)}^2=A+B$ if
$A^2+B^2+AB+BA=A+B$
if AB + BA = O
$i.e.$ if AB = BA = O