Involutory Matrix

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

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

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

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

Q.

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

1. B is idempotent

2. $AB=O$

3. $BA=O$

4. all of these

Q.

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

1. True

2. False