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Matrices and Determinants question

2025 · Shift 1 · Q20

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PYQ Library
JEE Advanced
Mathematics
Matrices and Determinants
2025 · Shift 1 · Q20

Matrices and Determinants question

2025 · Shift 1 · Q20

JEE AdvancedMathematicsMatrices and DeterminantsMCQ+3 / −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 \quad \text{and} \quad PQ = QP,

is

A
32
B
8
C
16
D
24

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