Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 25

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If $A$ is a $2 \times 2$ matrix and $A^{2} = I$ , where $A \neq I, A \neq - I$ , then of the following is necessarily true?

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Important Questions on Matrices

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 26

Let

A = [\begin{array}{l} 1 & 1 \\ 0 & 1 \end{array}]

and

P = [\begin{matrix} \cos \frac{π}{6} & \sin \frac{π}{6} \\ - \sin \frac{π}{6} & \cos \frac{π}{6} \end{matrix}]

and

Q = P A P^{⊤}

, then

P^{T} Q^{2013} P

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 27

If

A

is a square matrix, then

A

is symmetric, iff

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 28

If

A

is a square matrix, then

A

is skew-symmetric, iff

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 29

If

A

is any square matrix, then

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 30

If

A

and

B

are symmetric matrices of the same order, then

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 31

If

A

is any matrix then which of the following is not symmetric?

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 32

Each diagonal element of a skew symmetric matrix is

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Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 33

Let

A

be the set of all

3 \times 3

matrices which are symmetric with entries

0

or

1

. If there are five

1'

s and four

0'

s, then number of such matrices

A

is