Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 47

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If $A$ is an involuntary matrix given by $A = [\begin{array}{l} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{array}]$ then the inverse of $\frac{A}{2}$ will be

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Important Questions on Matrices

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 48

If

A

is a nonsingular matrix such that

A A^{T} = A^{T} A

and

B = A^{- 1} A^{T}

, then matrix

B

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 49

If

P

is an orthogonal matrix and

Q = P A P^{T}

and

x = P^{T} Q^{1000} P

, then

x^{- 1}

is, where

A

is involutaoy matrix

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 50

If

A

and

B

are two nonsingular matrices of the same order such that

B^{r} = I

, for some positive integer

r > I

, then

A^{- 1} B^{r - 1} A - A^{- 1} B^{- 1} A =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 51

If

adj B = A, |P| = |Q| = 1

, then

adj (Q^{- 1} B P^{- 1})

is,

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 52

If

A

is non-singular and

(A - 2 I) (A - 4 I) = O

, then

\frac{1}{6} A + \frac{4}{3} A^{- 1}

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 53

Let

f (x) = \frac{1 + x}{1 - x}

. If

A

is matrix for which

A^{3} = O,

then

f (A)

is

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 54

If

[\begin{matrix} 2 & 1 \\ 3 & 2 \end{matrix}] A [\begin{matrix} - 3 & 2 \\ - 3 & 5 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

, then

A =

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 13 - Matrices>Exercises>Q 55

If

A^{2} - A + I = 0,

then the inverse of

A

is