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

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

Matrices

Solution:

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