What is the binary number equivalent to decimal number 1011 ?

Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2^α 3^β, then what is the value of (α + β)? 

If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of $\left|\frac{\alpha^{100}+\beta^{100}}{\alpha^{100}-\beta^{100}}\right|$ ?

Let A and B be symmetric matrices of same order, then which one of the following is correct regarding (AB - BA) ?

1. Its diagonal entries are equal but nonzero

2. The sum of its non-diagonal entries is zero

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