If $A=\left(\begin{array}{lll}1& 0& 0\\ 0& 2& 0\\ 0& 0& 3\end{array}\right),$ then $adj(adjA)$ is equal to

Important Questions on Matrices and Determinants

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 43

If $A$ is a $3\times 3$ matrix such that $\left|A\right|=27, Adj\left(A\right)=k{A}^T,$ then $k^2-3k+5=$

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 44

If $A$ and $B$ are non-singular matrices, then

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 45

Matrix $A=\left[\begin{array}{ccc}1& 0& -k\\ 2& 1& 3\\ k& 0& 1\end{array}\right]$ is invertible for

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 46

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 

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 47

If $5$ and $7$ are the roots of the equation $\left|\begin{array}{lll}x& 4& 5\\ 7& x& 7\\ 5& 8& x\end{array}\right|=0,$ then what is the third root$?$

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 48

The matrix $A=\left[\begin{array}{ccc}1& 3& 2\\ 1& x-1& 1\\ 2& 7& x-3\end{array}\right]$ will have inverse for every real number $x$ except for

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 49

If $\left|\begin{array}{ccc}1& \cos \alpha & \cos \beta \\ \cos \alpha & 1& \cos \gamma \\ \cos \beta & \cos \gamma & 1\end{array}\right|=\left|\begin{array}{ccc}0& \cos \alpha & \cos \beta \\ \cos \alpha & 0& \cos \gamma \\ \cos \beta & \cos \gamma & 0\end{array}\right|$, then ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =$

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 50

If $A=\left[\begin{array}{ccc}9& 0& 0\\ {\alpha }^3& \alpha & 0\\ 7{\alpha }^2& 4{\beta }^4& 3\end{array}\right]$ and determinant of $A^3$ is $19683$, then the value of $\alpha$ is