Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 17

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IMPORTANT

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If $A$ is symmetric and $B$ is skew-symmetric matrix, then which of the following is/are CORRECT?

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Important Questions on Matrices

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 18

If

A = {(a_{i j})}_{n \times n}

and

f

is a function, we define

f (A) = {(f (a_{i j}))}_{n \times n}

. Let

A = (\begin{matrix} \frac{π}{2} - θ & θ \\ - θ & \frac{π}{2} - θ \end{matrix})

. Then

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 19

If

A

is a matrix such that

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

, then which of the following is/are true?

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 20

If

A = [\begin{matrix} 3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1 \end{matrix}],

then

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 21

If

[\begin{matrix} 1 & - \tan θ \\ \tan θ & 1 \end{matrix}] {[\begin{matrix} 1 & \tan θ \\ - \tan θ & 1 \end{matrix}]}^{- 1} = [\begin{matrix} a & - b \\ b & a \end{matrix}],

then

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 22

If

A^{- 1} = [\begin{matrix} 1 & - 1 & 2 \\ 0 & 3 & 1 \\ 0 & 0 & - \frac{1}{3} \end{matrix}]

, then

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 23

If

A

is an invertible matrix, then

{(adj A)}^{- 1}

is equal to

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 24

If

A

and

B

are two invertible matrices of the same order, then

a d j (A B)

is equal to

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 25

If

A, B

and

C

are three square matrices of the same order, then

A B = A C \Rightarrow B = C

. Then