Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 20

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If $A = [\begin{matrix} 1 & \tan x \\ - \tan x & 1 \end{matrix}]$ then let us define a function $f (x) = det (A^{T} A^{- 1})$ then which of the following can be the value,of $\underset{n t i m e s}{\underset{⏟}{f (f (f (f \dots \dots \dots . . f (x))))}} (n \geq 2)$

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Important Questions on Matrices and Determinants

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 21

If

A

and

B

are two invertible matrices of the same order, then

adj (A B)

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 22

If

A = [\begin{array}{l} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{array}], A^{- 1} = [\begin{matrix} 1 / 2 & - 1 / 2 & 1 / 2 \\ - 4 & 3 & c \\ 5 / 2 & - 3 / 2 & 1 / 2 \end{matrix}]

, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 23

If

A

and

B

are different matrices satisfying

A^{3} = B^{3}

and

A^{2} B = B^{2} A

, then which of the following is/are incorrect :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 24

If

A = [\begin{array}{l} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{array}]

, then-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 25

Let

Δ_{0} = |\begin{array}{l} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{array}|

(where

Δ_{0} \neq 0

) and let

Δ_{1}

denote the determinant formed by the cofactors of elements of

Δ_{0}

and

Δ_{2}

denote the determinant formed by the cofactors at

Δ_{n - 1}

then the determinant value of

Δ_{n}

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 26

A square matrix can always be expressed as a

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 27

Choose the correct answer :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 28

Let

a_{i j}

denote the element of the

i^{t h}

row and

j^{t h}

column in a

3 \times 3

matrix and let

a_{i j} = - a_{j j}

for every

i

and

j

then this matrix is an -