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List of top Mathematics Questions on Matrix

If \( P \) is a non-singular matrix of order \( 5 \times 5 \) and the sum of the elements of each row is 1, then the sum of the elements of each row in \( P^{-1} \) is:
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to: