If $A=\left[\begin{array}{ll}3& 2\\ 1& 4\end{array}\right]$, then $A\left(\mathrm{adj}A\right)=$

Important Questions on Matrices

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 13

If $A=\left[\begin{array}{cc}\cos x& \sin x\\ -\sin x& \cos x\end{array}\right]$, then $A(\mathrm{adj} A)=$

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 15

If $k$ is a scalar and $I$ is a unit matrix of order $3$, then $\mathrm{adj}\left(kI\right)=$

EASY

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 16

If $X$ is a square matrix of order $3\times 3$ and $\lambda$ is a scalar, then $\mathrm{adj}\left(\lambda X\right)$ is equal to

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 17

If $A$ is a singular matrix, then $adjA$ is

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 18

If $d$ is the determinant of a square matrix $A$ of order $n$, then the determinant of its adjoint is

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 19

If $A=\left[\begin{array}{ll}4& 2\\ 3& 4\end{array}\right]$, then $\mid adjA\mid$is equal to

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 20

For an invertible matrix $A$, if $A\left(adjA\right)=\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$, then $\left|A\right|=$

MEDIUM

MHT-CET

IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 10 - Matrices>Competitive Thinking>Q 21

If $A$ is a matrix of order $3$, such that $A\left(adjA\right)=10I$, then $\left|adjA\right|=$