let a be a 2 times 2 matrix statement 1 adj adj a a

Let $$A$$ be a $$2 \times 2$$ matrix
Statement - 1 : adj (adj $$A$$) = $$A$$
Statement - 2 : $$\left| {{\text{adj}}\,A} \right| = \left| A \right|$$

A. Statement - 1 is true, Statement - 2 is true. Statement - 2 is not a correct explanation for Statement - 1.

B. Statement - 1 is true, Statement - 2 is false.

C. Statement - 1 is false, Statement - 2 is true.

D. Statement - 1 is true, Statement - 2 is true. Statement - 2 is a correct explanation for Statement - 1.

Answer : Statement - 1 is true, Statement - 2 is true. Statement - 2 is a correct explanation for Statement - 1.

Solution :
We know that $$\left| {{\text{adj}}\left( {{\text{adj}}\,A} \right)} \right| = {\left| {{\text{adj}}\,A} \right|^{2 - 1}}$$
$$ = {\left| A \right|^{2 - 1}} = \left| A \right|$$
∴ Both the statements are true and statement - 2 is a correct explantion for statement - 1 .

Releted MCQ Question on
Algebra >> Matrices and Determinants

Releted Question 1

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

A. $$C$$ is empty

B. $$B$$ has as many elements as $$C$$

C. $$A = B \cup C$$

D. $$B$$ has twice as many elements as elements as $$C$$

View Answer

Releted Question 2

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

A. 0

B. 1

C. $$i$$

D. $$\omega $$

View Answer

Releted Question 3

Let $$a, b, c$$ be the real numbers. Then following system of equations in $$x, y$$ and $$z$$
$$\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1,$$ $$ - \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1$$ has

A. no solution

B. unique solution

C. infinitely many solutions

D. finitely many solutions

View Answer

Releted Question 4

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

A. $$A + B = B + A$$

B. $$A + B = A - B$$

C. $$A - B = B - A$$

D. $$AB=BA$$

View Answer

Let $$A$$ be a $$2 \times 2$$ matrix
Statement - 1 : adj (adj $$A$$) = $$A$$
Statement - 2 : $$\left| {{\text{adj}}\,A} \right| = \left| A \right|$$

Releted MCQ Question on
Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

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Matrices and Determinants

Practice More MCQ Question on Maths Section

Let $$A$$ be a $$2 \times 2$$ matrix Statement - 1 : adj (adj $$A$$) = $$A$$ Statement - 2 : $$\left| {{\text{adj}}\,A} \right| = \left| A \right|$$

Releted MCQ Question on Algebra >> Matrices and Determinants

Consider the set $$A$$ of all determinants of order 3 with entries 0 or 1 only. Let $$B$$ be the subset of $$A$$ consisting of all determinants with value 1. Let $$C$$ be the subset of $$A$$ consisting of all determinants with value $$- 1.$$ Then

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then \[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

If $$A$$ and $$B$$ are square matrices of equal degree, then which one is correct among the followings?

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Practice More MCQ Question on Maths Section

Let $$A$$ be a $$2 \times 2$$ matrix
Statement - 1 : adj (adj $$A$$) = $$A$$
Statement - 2 : $$\left| {{\text{adj}}\,A} \right| = \left| A \right|$$

Releted MCQ Question on
Algebra >> Matrices and Determinants

If $$\omega \left( { \ne 1} \right)$$ is a cube root of unity, then
\[\left| {\begin{array}{*{20}{c}} 1&{1 + i + {\omega ^2}}&{{\omega ^2}}\\ {1 - i}&{ - 1}&{{\omega ^2} - 1}\\ { - i}&{ - i + \omega - 1}&{ - 1} \end{array}} \right|=\]

Practice More Releted MCQ Question on
Matrices and Determinants