JEE Advance 2025 Paper 1

Consider the matrix $P = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}$  . Let the transpose of a matrix $X$   be denoted by $X^{T}$  . Then the number of $3 \times 3$   invertible matrices $Q$   with integer entries, such that $Q^{-1} = Q^{T}$   and $PQ = QP$  , is