Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 97

EASY

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IMPORTANT

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Assertion(A) : If $A$ is invertible square matrix, then $A^{T}$ is invertible

Reason(R) : Inverse of invertible symmetric matrix is symmetric matrix.

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Important Questions on Matrices

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 98

If

A = (\begin{matrix} 2 x & 0 \\ x & x \end{matrix})

and

A^{- 1} = (\begin{matrix} 1 & 0 \\ - 1 & 2 \end{matrix})

then

x =

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 99

Matrices

A

and

B

are inverses of each other only when

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 101

If

A

is a square matrix such that

| A | \neq 0

and

A^{2} - A + 2 I = O

, then

A^{- 1} =

?

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 102

If

A = [\begin{array}{l} 1 & λ & 2 \\ 1 & 2 & 5 \\ 2 & 1 & 1 \end{array}]

is not invertible, then

λ =

?

EASY

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 103

If

A

and

B

are invertible square matrices of the same order then

{(A B)}^{- 1} =

?

MEDIUM

CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 104

The inverse of

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

is

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 108

If

(A B)^{- 1} = [\begin{matrix} 12 & - 17 \\ - 19 & 27 \end{matrix}]

and

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

then

B^{- 1} =

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 3 - Matrices>Exercise>Q 109

If

A^{T} A^{- 1}

is symmetric, then

A^{2} =