Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 22

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If $d$ is the determinant of a square matrix $A$ of order $n$ , then the determinant of its adjoint is

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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 23

If

A

is a singular matrix, then

a d j A

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 24

If

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

, then

A (adj A) =

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 25

If

A = [\begin{matrix} 2 & - 3 \\ - 4 & 1 \end{matrix}]

, then

adj (3 A^{2} + 12 A)

is equal to

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 26

If

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

, then the value of

|A| |adj A|

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 27

If

A = [\begin{array}{l} 4 & 2 \\ 5 & 3 \end{array}]

, then

|a d j (a d j (A))|

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 28

The adjoint of the matrix

A = [\begin{array}{l} 1 & 0 & 2 \\ 2 & 1 & 0 \\ 0 & 3 & 1 \end{array}]

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 29

Which of the following statements is false:

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 30

If

A = [\begin{matrix} 1 & - 1 & 1 \\ 0 & 2 & - 3 \\ 2 & 1 & 0 \end{matrix}], B = adj A

and

C = 5 A

, then

\frac{| adj B |}{| C |} =