23. If A, B are two idempotent matrices and
AB = BA=0 then A+B is
1) Scalar matrix
Idempotent matrix
3) Diagonal matrix 4) Nilpotent matrix
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Answer:
2) Idempotent matrix.
Step-by-step explanation:
A and B are two Idempotent matrices are square matrices :
A² = A × A = A , B² = B × B = B
Given
A × B = O and B × A = O = zero matrix.
As A and B are square matrices of the same order (as their product is defined), let us add them.
Now Find
(A+B) × (A+B) = A² + A × B + B × A + B²
= A + O + O + B
= A + B
Hence , A + B is also idempotent matrix.
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