Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 11

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If $A$ is a diagonal matrix of order $3 \times 3$ is commutative with every square matrix of order $3 \times 3$ under multiplication and $tr (A) = 12$ then the value of $d t . (A)$ is.

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Important Questions on Matrices

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 12

If

A

is a square matrix of order

3

such that

|A| = 2,

then

|{(a d j A^{- 1})}^{- 1}|

is

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

If

A and B

are two matrices of order

3

such that

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

, then

tr (A^{2} + B^{2})

is equal to.

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 14

If

a, b and c

are integers, then number of matrices

A = [\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix}]

which are possible such that

A A^{T} = I

is.

HARD

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 15

Let

A = [a_{i j}] b e 3 \times 3

matrix and

B = [b_{i j}] b e 3 \times 3

matrix such that

b_{i j}

is the sum of the elements of

i^{th}

row of

A

except

a_{i j} .

If

\det (A) = 19

, then the value of

\det (B)

is .

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 16

A square matrix

M

of order

3

satisfies

M^{2} = I - M,

where

I

is an identity matrix of order

3 .

If

M^{n} = 5 I - 8 M,

then

n

is equal to.

HARD

JEE Main/Advance

IMPORTANT

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

Let

A = {[a_{i j}]}_{3 \times 3}, B = {[b_{i j}]}_{3 \times 3} a n d C = {[c_{i j}]}_{3 \times 3}

be any three matrices, where

b_{i j} = 3^{i - j} a_{i j} and c_{i j} = 4^{i - j} b_{i j .}

If

d e t . A = 2,

then

\det (B C)

is equal to .

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IMPORTANT

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

If

A

is a square matrix of order

2 \times 2

such that

|A| = 27,

then sum of the infinite series

|A| + |\frac{1}{2} A| + |\frac{1}{2} A| + |\frac{1}{8} A| + . . .

is equal to.

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IMPORTANT

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

If

A

is a square matrix of order

2

and

\det (A) = 10

, then

({(tr A)}^{2} - tr (A^{2}))

is equal to.