The set of all $2 \times 2$ matrices which commute with the $\left[ {\begin{array}{*{20}{c}} 1&1 \\ 1&0 \end{array}} \right]$ with respect to matrix multplication is

$\left\{\left[\begin{array}{ll}p & q \\ r & r\end{array}\right]: p, q, r \in R\right\}$

$\left\{\left[\begin{array}{ll}p & q \\ 4 & r\end{array}\right]: p, q, r \in R\right\}$

$\left\{\left[\begin{array}{cc}p-q & p \\ q & r\end{array}\right]: p, q, r \in R\right\}$

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JEE MATHEMATICS MCQ: MATRICES

1 Hard

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Application +4 | -1

The set of all

2 \times 2

matrices which commute with the

\left[ {\begin{array}{cccccccccccccccccccc} 1&1 \\ 1&0 \end{array}} \right]

with respect to matrix multplication is

View answer and explanation

Correct option: D

\left\{\left[\begin{array}{cc}p & q \\ q & p-q\end{array}\right]: p, q \in R\right\}

Option D is the correct answer because it represents the set of all 2x2 matrices that commute with the given matrix, derived by equating AB and BA and solving for the matrix elements.

More Questions from MATRICES

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\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

and

a, b, c

are real numbers then the line

a x+b y+c=0

passes through the fixed point is The number of solutions of the system of equations

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

is If the equations

2x + 3y + 1 = 0,3x + y - 2 = 0

and

ax + 2y - b = 0

are consistent, then The value of the determinant

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

, is If

\omega

is the cube root of unity, then

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

is equal to For any matrix

A

of order

2 \times 2

, if

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

, then

|A|

is equal to