If A- a b c x y z p q r - -B- q -b y -p a -x r -c z - and A is invertible - then which of the following is not true-

The correct option is A |A|=|B|Hence, #160;option (A) is correct answer. ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

If A=[ a ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} q & - b & y - p & a & - x r & - c & z \end{matrix} ⎤ ⎥ ⎦$ and A is invertible , then which of the following is not true?

|A|=|B|

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|A|=-|B|

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|adiA|=|adiB|

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A is invertivlbe if and only when B is invertible

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Solution

The correct option is A |A|=|B|
Hence, option $(A)$ is correct answer.

Suggest Corrections

Similar questions

Q.
If

A = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ∣ ∣ ∣ ∣

and

B = ∣ ∣ ∣ ∣ \begin{matrix} q & - b & y - p & a & - x r & - c & z \end{matrix} ∣ ∣ ∣ ∣

, then

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} q & - b & y - p & a & - x r & - c & z \end{matrix} ⎤ ⎥ ⎦

and if

A

is invertible, then which of the following is/are true:

Q. We define a binary relation

\sim

on the set of all

3 \times 3

matrices as

A \sim B

if and only if there exist invertible matrices

P

and

Q

such that

B = P A Q^{- 1}

. The binary relation

\sim

Q. We define a binary relation

\sim

on the set of all

3 \times 3

real matrices as

A \sim B

, if and only if there exist invertible matrices

P

and

Q

such that

B = P A Q^{- 1}

. The binary relation

\sim

Q. Let

f : [0, \infty) \to R

be a function defined by

f (x) = 9 x^{2} + 6 x - 5

. Prove that f is not invertible. Modify, only the codomain of f to make f invertible and then find its inverse.

OR

Let

*

be a binary operation defined on

Q \times Q

(a, b) * (c, d) = (a c, b + a d)

, where Q is the set of rational numbers. Determine whether

*

is commutative and associative. Find the identity element for

*

and the invertible elements of

Q \times Q

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If A=⎡⎢⎣abcxyzpqr⎤⎥⎦,B=⎡⎢⎣q−by−pa−xr−cz⎤⎥⎦ and A is invertible , then which of the following is not true?

The correct option is A |A|=|B|Hence, option (A) is correct answer.

If $A = ⎡ ⎢ ⎣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} q & - b & y - p & a & - x r & - c & z \end{matrix} ⎤ ⎥ ⎦$ and A is invertible , then which of the following is not true?

The correct option is A |A|=|B|
Hence, option $(A)$ is correct answer.