Involutory Matrix

Q.

If A is an idempotent matrix and A + B =I, then which of the following is true?

1. $BA=O$

2. all of these

3. B is idempotent

4. $AB=O$

Q. If A is involutary matrix, then which of the following is/are correct?

1. $\frac{I+A}{3}$ is idempotent
2. (I + A)(I – A) is singular
3. I – A is idempotent
4. I + A is idempotent

Q.

$\text{A =}\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\text{is an involutary matrix.}$

1. False

2. True

Q.

If A is an idempotent matrix and A + B =I, then which of the following is true?

1. B is idempotent

2. $BA=O$

3. $AB=O$

4. all of these

Q. If A is a non-diagonal involutory matrix, then

1. A - I = 0
2. A - I is non zero singular
3. A + I = 0
4. none of these