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## MCQ (More than One Correct Answer)

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Let $$\Delta = \left| {\matrix{ {\sin \theta \cos \phi } & {\sin \theta \sin \phi } & {\cos \theta } \cr {\cos ... WB JEE 2022$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1} \cr {7x - 2} & {17x + 6} & {12x -...
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The solution of $$\det (A - \lambda {I_2}) = 0$$ be 4 and 8 and $$A = \left( {\matrix{ 2 & 2 \cr x & y \cr }... WB JEE 2022 If$$A = \left( {\matrix{ 1 & 1 \cr 0 & i \cr } } \right)$$and$${A^{2018}} = \left( {\matrix{ a & b \c...
WB JEE 2022
If $$p = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint ...
WB JEE 2022
If $$\Delta (x) = \left| {\matrix{ {x - 2} & {{{(x - 1)}^2}} & {{x^3}} \cr {x - 1} & {{x^2}} & {{{(x + 1)}^3}} ... WB JEE 2022 Under which of the following condition(s) does(do) the system of equations$$\left( {\matrix{ 1 & 2 & 4 \cr 2 & ...
WB JEE 2022
The determinant $$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} & {{b^2} + 10} & {bc} \cr {ac} & {bc... WB JEE 2021 Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 ... WB JEE 2021 If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{ {\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} ...
WB JEE 2021
Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to ...
WB JEE 2021
Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr 0 & { - \sin t} & {\cos t} \cr } }... WB JEE 2021 If M is a 3$$\times$$3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to WB JEE 2021 If the vectors$$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha...
WB JEE 2020
If f : S $$\to$$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{ ... WB JEE 2020 If$$\left| {\matrix{ {{a^2}} &amp; {bc} &amp; {{c^2} + ac} \cr {{a^2} + ab} &amp; {{b^2}} &amp; {ca} \cr {...
WB JEE 2020
Let $$A = \left( {\matrix{ a &amp; b \cr c &amp; d \cr } } \right)$$ be a 2 $$\times$$ 2 real matrix with ...
WB JEE 2020
Let $$A = \left[ {\matrix{ {12} &amp; {24} &amp; 5 \cr x &amp; 6 &amp; 2 \cr { - 1} &amp; { - 2} &amp; 3 \... WB JEE 2020 Let A =$$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matrix{ {} \cr {} \cr {} \cr ...
WB JEE 2020
$$\left| {\matrix{ {a - b} & {b - c} & {c - a} \cr {b - c} & {c - a} & {a - b} \cr {c - a} & {a - b} & {b -... WB JEE 2011 If one of the cube roots of 1 be$$\omega$$, then$$\left| {\matrix{ 1 & {1 + {\omega ^2}} & {{\omega ^2}} \cr {...
WB JEE 2011
If $$z = \left| {\matrix{ 1 & {1 + 2i} & { - 5i} \cr {1 - 2i} & { - 3} & {5 + 3i} \cr {5i} & {5 - 3i} & 7 ... WB JEE 2011 If$$A = \left( {\matrix{ 3 & {x - 1} \cr {2x + 3} & {x + 2} \cr } } \right)$$is a symmetric matrix, then t... WB JEE 2011 If A and B are two matrices such that A + B and AB are both defined, then WB JEE 2011 If$$A = \left[ {\matrix{ 1 & 2 \cr { - 4} & { - 1} \cr } } \right]$$then A$$-$$1 is WB JEE 2010 If$$\omega$$is an imaginary cube root of unity and$$\left| {\matrix{ {x + {\omega ^2}} & \omega & 1 \cr \ome...
WB JEE 2010
If the matrices $$A = \left[ {\matrix{ 2 & 1 & 3 \cr 4 & 1 & 0 \cr } } \right]$$ and $$B = \left[ {\matrix{ ... WB JEE 2010 If A and B are square matrices of the same order and AB = 3I, then A$$-$$1 is equal to WB JEE 2009 If A2$$-$$A + I = 0, then the inverse of the matrix A is WB JEE 2009 If A is a square matrix. Then WB JEE 2009 If the matrix$$\left[ {\matrix{ a & b \cr c & d \cr } } \right]$$is commutative with the matrix$$\left[ {...
WB JEE 2008
The values of x for which the given matrix \left[ {\matrix{ { - x} & x & 2 \cr 2 & x & { - x} \cr x & { -...
WB JEE 2008

## Subjective

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If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B.
WB JEE 2010

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