If $A=\left[\begin{array}{rrr}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$, then $A^{-1}=$

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 40

If $A={\left[a_{ij}\right]}_{2\times 2}$, where $a_{ij}=\left\{\begin{array}{ll}i+j,& \mathrm{if} i\ne j\\ i^2-2j,& \mathrm{if} i=j\end{array}\right.$ then ${\mathrm{A}}^{-1}$ is equal to 

HARD

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 41

The element of second row and third column in the inverse of $\left[\begin{array}{ccc}1& 2& 1\\ 2& 1& 0\\ -1& 0& 1\end{array}\right]$ is

HARD

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 42

The element in the first row and third column of the inverse of the matrix $\left[\begin{array}{ccc}1& 2& -3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$ is

HARD

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 43

If $A=\left[\begin{array}{lll}0& 1& 2\\ 1& 2& 3\\ 3& 1& 1\end{array}\right],$ then the sum of all the diagonal entries of $A^{-1}$ 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 44

If Matrix $A=\left[\begin{array}{ll}1& 2\\ 4& 3\end{array}\right]$ such that $Ax=I,$ then $x=\_\_\_\_\_\_\_\_$

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 45

The matrix $A$ satisfying $A\left[\begin{array}{ll}1& 5\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}3& -1\\ 6& 0\end{array}\right]$ 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 46

If $A=\left[\begin{array}{ll}3& 2\\ 0& 1\end{array}\right],$ then ${\left(A^{-1}\right)}^3$ is equal to

HARD

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 47

$A=\left[\begin{array}{ll}0& 3\\ 2& 0\end{array}\right]$ and $A^{-1}=\lambda \left(adj\right(A\left)\right),$ then $\lambda =$