List of top Mathematics Questions on Determinants asked in IIT JAM MA

Let \( M\in M_3(\mathbb{R}) \). If

Let \(P\) be a \(5\times 5\) real matrix with \(\det(P)=2\). Let \(Q\) be the matrix of cofactors of \(P\). Then \(\det(Q)=\underline{}\) rounded off to one decimal place.

Let \( M \) and \( N \) be any two \( 4 \times 4 \) matrices with integer entries satisfying

\[ MN = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{pmatrix} = 2 \]

Then the maximum value of \( \det(M) + \det(N) \) is ...............