What is the principal value branch of the inverse trigonometric function $f (x) = sin^{- 1} x$ ?

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Let $R$ be a binary relation defined on a non-empty set $A$ . Under which condition is $R$ classified as an equivalence relation?
What is the exact principal value of $cos^{- 1} (- \frac{1}{2}) + 2 sin^{- 1} (\frac{1}{2})$ ?
For two conformable square matrices $A$ and $B$ , which of the following expressions is always identical to $(A B)^{T}$ ?
What is the value of all main diagonal elements in any real skew-symmetric matrix $A$ ?
If $A$ is an invertible square matrix of order $3 \times 3$ with determinant $∣ A ∣ = 4$ , what is the value of $∣2 A ∣$ ?
If $A$ is a non-singular square matrix of order $3 \times 3$ with determinant $∣ A ∣ = 5$ , what is the value of $∣ adj (A) ∣$ ?

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