Let $A = \left[ {\begin{array}{*{20}{c}} 0&{ - 2} \\ 2&0 \end{array}} \right]\,$ If $M$ and $N$ are two matrices given by $M = \sum\limits_{k = 1}^{10} {{A^{2k}}} $ and $N = \sum\limits_{k = 1}^{10} {{A^{2k - 1}}} $ then $M{N^2}$ is

Neither symmetric nor skew-symmetric matrix

JEE MATHEMATICS MCQ: MATRICES

1 Easy

1 of 1

Analyzing +4 | -1

Let

A = \left[ {\begin{array}{cccccccccccccccccccc} 0&{ - 2} \\ 2&0 \end{array}} \right]\,

M

and

N

are two matrices given by

M = \sum\limits_{k = 1}^{10} {{A^{2k}}}

and

N = \sum\limits_{k = 1}^{10} {{A^{2k - 1}}}

then

M{N^2}

View answer and explanation

Correct option: A

A non-identity symmetric matrix

The correct answer is A (A non-identity symmetric matrix) because after calculating A², M and N can be expressed in terms of I and A, and MN² simplifies to a scalar multiple of the identity matrix, which is symmetric.

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