Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 9

HARD

JEE Main

IMPORTANT

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Let $A$ and $B$ be two non-singular square matrices, such that $B \neq I$ and $A B^{2} = B A$ . If $A^{3} = B^{- 1} A^{3} B^{n}$ , then the value of $n$ is

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Important Questions on Matrices

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 10

If

A

is an idempotent matrix satisfying

(I - 0.4 A)^{- 1} = I - α A

(where

I

is the unit matrix of the same order as that of

A

), then the value of

α

is

EASY

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 11

If

A

and

B

are two non-singular matrices which commute, then

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

is equal to

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 12

If

A

and

B

are non-singular matrices of order

n \times n

, such that

3 A B A^{- 1} + A = 2 A^{- 1} B A

, then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 13

If the matrices

A

and

B

are of

3 \times 3

and

(I - A B)

is invertible, then which of the following statement(s) is/are correct?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 14

If

A

is a square matrix, such that

A . (adj A) = [\begin{array}{l} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}]

, then