Matrices & Determinants: JEE Main Mathematics Previous Year Questions

565 previous year questions from Matrices & Determinants. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.For the matrices $A=\left(\begin{array}{cc}3& -4\\ 1& -1\end{array}\right)$ and $B=\left(\begin{array}{cc}-29& 49\\ -13& 18\end{array}\right)$, if…
2. 2.The inverse of the matrix $\left(\begin{array}{ccc}1& 0& 0\\ 3& 3& 0\\ 5& 2& -1\end{array}\right)$ is
3. 3.If the system of equations $x+2y+3z=3$ $4x+3y-4z=4$ $8x+4y-\text{λz}=9+\mu$ has infinitely many solutions, then the ordered pair…
4. 4.Let $\alpha \text{∈}\text{(}0\text{,}\infty \text{)}$ and $A=\left(12\alpha 101012\right)$. If…
5. 5.If P is a $3\times 3$ real matrix such that $P^T=\text{aP}+(a-1)I\text{,}$ Where $a>1$, then
6. 6.If $A=\left(\begin{array}{cc}0& 3\\ 0& 0\end{array}\right)$ and $f(x)=x+x^2+x^3+\dots +x^{2023}$ then $f(A)+I=$
7. 7.The value of determinant $\left|\begin{array}{ccc}a-b& b+c& a\\ b-a& c+a& b\\ c-a& a+b& c\end{array}\right|$ is
8. 8.If $A=(12-1-102120)$ and $B=(-3-2422-1-203)$, then $A^2=$
9. 9.If $A=\left(\begin{array}{cccc}2& 1& 3& -1\\ 1& -2& 2& -3\end{array}\right)$, $B=\left(\begin{array}{cccc}2& 1& 0& 3\\ 1& -1& 2& 3\end{array}\right)$ and $2A+3B-5C=0$, then $C=$
10. 10.The value of $\left|\begin{array}{cc}{\log }_{5}729& {\log }_{3}5\\ {\log }_{5}27& {\log }_{9}25\end{array}\right|\times \left|\begin{array}{cc}{\log }_{3}5& {\log }_{27}5\\ {\log }_{5}9& {\log }_{5}9\end{array}\right|$ is
11. 11.The characteristic roots of the matrix $\left(\begin{array}{ccc}1& 0& 0\\ 2& 3& 0\\ 4& 5& 6\end{array}\right)$ are
12. 12.The area of a triangle with vertices $\text{(}-3\text{,}0\text{)}$, $\text{(}3\text{,}0\text{)}$ and $\text{(}0\text{,}k\text{)}$ is 9 sq. units, the value of $k$ is
13. 13.The value of $\left|\begin{array}{ccc}1& {\log }_{x}y& {\log }_{x}z\\ {\log }_{y}x& 1& {\log }_{y}z\\ {\log }_{z}x& {\log }_{z}y& 1\end{array}\right|=$
14. 14.If $\left(\alpha \beta \gamma \right)=(\text{cos}\text{⁡}\theta -\text{sin}\text{⁡}\theta 0\text{sin}\text{⁡}\theta \text{cos}\text{⁡}\theta 0001)\left(xyz\right)$, then…
15. 15.Let m and M be respectively the minimum and maximum values of…
16. 16.The constant term in the expansion of $\left|\begin{array}{ccc}3x+1& 2x-1& x+2\\ 5x-1& 3x+2& x+1\\ 7x-2& 3x+1& 4x-1\end{array}\right|$ is
17. 17.If the system of equations $3x+y+4z=32x+\text{αy}-z=-3x+2y+z=4$has no solution, then the value of $\alpha$ is equal to :
18. 18.If $A=\left(\begin{array}{ccc}1& 3& -2\\ -3& 0& -5\\ 2& 5& 0\end{array}\right)$ and $A(\mathrm{adj}A)=KI$, then the value of $K$ is (where $I$ is unit matrix of order 3)
19. 19.Let A be a $3\times 3$ matrix such that adj$A=(2-11-1021-2-1)$and $B=\text{adj}\left(\text{adj}A\right)$. If $\left(A\right)=\lambda$ and…
20. 20.If $A=\left(\begin{array}{cc}2& 3\\ 0& -1\end{array}\right)$ then the value of $\det (A^4)+\det \left(A^{10}-(\mathrm{Adj}(2A){)}^{10}\right)$ is equal to
21. 21.Let $A=\left(\begin{array}{cc}\frac{1}{\sqrt{10}}& \frac{3}{\sqrt{10}}\\ \frac{-3}{\sqrt{10}}& \frac{1}{\sqrt{10}}\end{array}\right)$ and $B=\left(\begin{array}{cc}1& -i\\ 0& 1\end{array}\right)$, where…
22. 22.Let $M$ be $2\times 2$ symmetric matrix with integer entries, then $M$ is invertible if
23. 23.If $a+x=b+y=c+z+1$, where $a,b,c,x,y,z$ are non-zero distinct real numbers, then $\left|\begin{array}{ccc}x& a+y& x+a\\ y& b+y& y+b\\ z& c+y& z+c\end{array}\right|$ is equal to:
24. 24.The values of $m\text{,}n$, for which the system of equations $x+y+z=4\text{,}2x+5y+5z=17\text{,}x+2y+mz=n$ has infinitely many solutions, satisfy the equation:
25. 25.Let $A=\left(x110\right)\text{,}x\text{∈}R$and $A^4=\left(a_{\text{ij}}\right)$. If $a_{11}=109$, then $a_{22}$ is equal to