With usual notations, in $\triangle ABC$, if $\cos C = \dfrac{\sin A}{2\sin B}$, then which of the following is true ?

In $\triangle ABC$, if $a = 13, b = 14, c = 15$, then the value of $\sin A + \cos A$ is...

If the matrix $A = \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix}$ is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?

If $A$ is a non-singular matrix and $A^2 - A + I = 0$, then $A^{-1} = \ldots$