Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 10

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If $A$ and $B$ are square matrices of same order and $A A^{T} = I$ then ${(A^{T} B A)}^{10}$ is equal to -

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Important Questions on Matrices and Determinants

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 11

A square matrix

A

is called orthogonal, if (

A^{'}

is the transpose of

A

)

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 12

How many

3 \times 3

skew-symmetric matrices can be formed using numbers

- 2, - 1, 1, 2, 3, 4, 0

(any number can be used any number of times but

0

can be used at most

3

times)

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 13

Number of

3 \times 3

non-symmetric matrix

A

such that

A^{T} = A^{2} - I

and

| A | \neq 0,

equals to

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 14

If A is an orthogonal matrix &

| A | = - 1

, then

A^{T}

is equal to-

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 16

Which of the following is not true?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 17

Let

A = [\begin{array}{l} x & y & z \\ y & z & x \\ z & x & y \end{array}],

where

x, y

and

z

are real numbers such that

x + y + z > 0

and

x y z = 2

. If

A^{2} = I_{3}

, then the value of

x^{3} + y^{3} + z^{3}

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 18

Let

A

be a symmetric matrix of order

2

with integer entries. If the sum of the diagonal elements of

A^{2}

is

1,

then the possible number of such matrices is:

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 2>Q 14

A square matrix

A = [\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}],

then which of the following statement is not correct?