Consider the matrix P = ( array lll 2 & 0 & 0 0 & 2 & 0 0 & 0 & 3 array ) . Let the…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
Consider the matrix \[\boldsymbol{P}=\left(\begin{array}{lll}
2 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 3
\end{array}\right)\].
Let the transpose of a matrix X be denoted by XT. Then the number of 3 × 3 invertible matrices Q with integer entries, such that Q–1 = QT and PQ = QP, is
Let the transpose of a matrix X be denoted by XT. Then the number of 3 × 3 invertible matrices Q with integer entries, such that Q–1 = QT and PQ = QP, is
- 32
- 8
- 16
- 24
Answer
(C) 16
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