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Matrices and Determinants question

2025 · Shift 2 · Q21

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JEE Advanced
Mathematics
Matrices and Determinants
2025 · Shift 2 · Q21

Matrices and Determinants question

2025 · Shift 2 · Q21

JEE AdvancedMathematicsMatrices and DeterminantsMultiple correct+4 / −2

Let

I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)

and

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

. Let

Q=\left(\begin{array}{ll}x & y \\ z & 4\end{array}\right)

for some non-zero real numbers

x, y

, and

z

, for which there is a

2 \times 2

matrix

R

with all entries being non-zero real numbers, such that

Q R=R P

. Then which of the following statements is (are) TRUE?

A
The determinant of $Q - 2I$ is zero
B
The determinant of $Q - 6I$ is 12
C
The determinant of $Q - 3I$ is 15
D
$yz = 2$

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