If $$E(\theta ) = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$, then E($$\alpha$$) E($$\beta$$) is equal to

If A is an orthogonal matrix of order 3 and $$B = \left[ {\matrix{ 1 & 2 & 3 \cr { - 3} & 0 & 2 \cr 2 & 5 & 0 \cr } } \right]$$, then which of the following is/are correct?

1. $$\left| {AB} \right| = \pm \,47$$ 2. AB = BA

Select the correct answer using the code given below.

If $$A = \left[ {\matrix{ 1 & { - 1} \cr 2 & 3 \cr } } \right]$$ and $$B = \left[ {\matrix{ 2 & 3 \cr { - 1} & { - 2} \cr } } \right]$$, then which of the following is/are correct?

I. AB (A^$$-$$1 B^$$-$$1) is a unit matrix.

II. (AB)^$$-$$1 = A^$$-$$1 B^$$-$$1.

Select the correct answer using the code given below.

Consider the following in respect of the matrix $$A = \left[ {\matrix{ { - 1} & 1 \cr 1 & { - 1} \cr } } \right]$$

1. A² = $$-$$ A

2. A³ = 4A

Which of the above is/are correct?