Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 3

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A square matrix $P$ satisfies $P^{2} = I - P$ , where $I$ is identity matrix. If $P^{n} = 5 I - 8 P$ , then $n$ is equal to

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Important Questions on Matrices

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 4

A

and

B

are two square matrices such that

A^{2} B = B A

and if

(A B)^{10} = A^{k} B^{10},

then $k$ is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 5

If matrix

A = {[a_{i j}]}_{3 \times 3},

matrix

B = {[b_{i j}]}_{3 \times 3},

where

a_{i j} + a_{j i} = 0

and

b_{i j} - b_{j i} = 0 \forall i, j

, then

A^{4} \cdot B^{3}

is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 6

If

A (\begin{matrix} 1 & 3 & 4 \\ 3 & - 1 & 5 \\ - 2 & 4 & - 3 \end{matrix}) = (\begin{matrix} 3 & - 1 & 5 \\ 1 & 3 & 4 \\ 4 & - 8 & 6 \end{matrix})

, then

A =

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 7

Let

A = [\begin{matrix} - 5 & - 8 & - 7 \\ 3 & 5 & 4 \\ 2 & 3 & 3 \end{matrix}]

and

B = [\begin{array}{l} x \\ y \\ 1 \end{array}]

, if

A B = λ B (λ \in R, λ \neq 0)

, then the value of

x + y

can be

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Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 8

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

and

MA = A^{2 m}, m \in N

for some matrix

M

then which one of the following is correct?

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

If

A = {[a_{i j}]}_{m \times n}

,

a_{i j} = (i^{2} + j^{2} - i j) (j - i)

and

n

is odd, then which of the following is not the value of

Tr (A)

?

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

|A - B| \neq 0, A^{4} = B^{4}, C^{3} A = C^{3} B, B^{3} A = A^{3} B,

then

|A^{3} + B^{3} + C^{3}| =

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

If $A B + B A = 0,$ then which of the following is equivalent to $A^{3} - B^{3}$ .