jee-advanced 2025 Q4

jee-advanced · India · paper1 3 marks 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning
Consider the matrix
$$P = \left( \begin{array} { l l l } 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{array} \right)$$
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
$$Q ^ { - 1 } = Q ^ { T } \text { and } P Q = Q P$$
is
(A)32(B)8(C)16(D)24
Consider the matrix

$$P = \left( \begin{array} { l l l } 
2 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 3
\end{array} \right)$$

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

$$Q ^ { - 1 } = Q ^ { T } \text { and } P Q = Q P$$

is

\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
(A) & 32 & (B) & 8 & (C) & 16 & (D) & 24 \\
\hline
\end{tabular}
\end{center}