Matrices and Determinants PYQs - Last 5 Years

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Practice 83 MHT CET Mathematics questions from Matrices and Determinants. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Matrices and Determinants Questions

Showing 33 of 83 filtered questions.

1Matrices And Determinants

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofactors is

2Matrices And Determinants

Suppose A is any $3 \times 3$ non-singular matrix and $(\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=0$ where $\mathrm{I}=\mathrm{I}_3$ and $\mathrm{O}=\mathrm{O}_3$. Here $\mathrm{O}_3$ represent zero matrix of order 3 and $\mathrm{I}...

3Matrices And Determinants

Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}_2$, (where $\mathrm{I}_2$ is unit matrix of order 2), then

4Matrices And Determinants

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

5Matrices And Determinants

For the system $x-y+z=4,2 x+y-3 z=0$, $x+y+z=2$, the values of $x, y, z$ respectively are given by

6Matrices And Determinants

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

7Matrices And Determinants

Let $X=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mathrm{A}=\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}3 \\ 1 \\ 4\end{array}\r...

8Matrices And Determinants

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in \mathbb{R}^{+}$and $A^4=\left[a_{i j}\right]_2$.
If $a_{11}=109$, then $\left(A^4\right)^{-1}=$

9Matrices And Determinants

If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$, $\bar{c}=c_1 \hat{i}+c_2 \hat{j}+c_3 \hat{k}$ and $\left[\begin{array}{lll}3 \bar{a}+\bar{b} & 3 \bar{b}+\bar{c} & 3 \bar{c}+\bar{a}\end{ar...

10Matrices And Determinants

Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha, \beta \in \mathbb{R}$, I is the identity matrix of order 2 , then $4(\alpha-\beta)$ is

11Matrices And Determinants

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $\left(A^2 B^2-B^2 A^2\right) X=O$. where $X$ is $3 \times 1$ column matrix of unknown variables a...

12Matrices And Determinants

If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ is equal to

13Matrices And Determinants

Let $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$ such that $\mathrm{AX}=\mathrm{B}$, then $\mathrm{X}=$

14Matrices And Determinants

If $A\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is

15Matrices And Determinants

If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is symmetric and $B$ is skew-symmetric matrix, then the matrix $\left(A^{-1} B+A B^{-1}\right)$ at $\theta=\frac{\pi}{6}$ is...

16Matrices And Determinants

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

17Matrices And Determinants

If $\mathrm{w}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$ where $\mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ is

18Matrices And Determinants

If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of \(\left(2 A^2+5 A\right)\) is

19Matrices And Determinants

Let $$A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], B=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]$$ and $$X=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]$$, if \(\mathrm{AX}=\mathrm{B}\), t...

20Matrices And Determinants

If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$$, then the value of \(B\) is

21Matrices And Determinants

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right].$$ If \(B=I-{ }^3 C_1(\operatorname{adj} A)+{ }^3 C_2(\operatorname{adj} A)^2-{ }^3 C_3(\operatorname{adj} A)^3\), then the sum of all elements of the matrix B is

22Matrices And Determinants

If $$A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 1 \\ 4 & -1\end{array}\right]$$, then \((A+B)^{-1}\) is

23Matrices And Determinants

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$ and \(A_{i j}\) is a cofactor of \(a_{i j}\) then the value of \(a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}\) is

24Matrices And Determinants

If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then \(A^T \cdot A^{-1}=\)

25Matrices And Determinants

If the matrix $$\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$$ and \(\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}\), when \(I\) is a unit matrix of order 2 , then the value of \(2 x+3 y\) is

26Matrices And Determinants

If $$A=\left[\begin{array}{cc}2 a & -3 b \\ 3 & 2\end{array}\right]$$ and \(A \cdot \operatorname{adj} A=A A^T\), then \(2 a+3 b\) is

27Matrices And Determinants

Let \(\omega \neq 1\) be a cube root of unity and \(S\) be the set of all non-singular matrices of the form $$\left[\begin{array}{ccc}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$$ where each of \(a, b\) and \(c\) ...

28Matrices And Determinants

If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a \(3 \times 3\) matrix \(A\) and \(|A|=4\), then value of \(\alpha\) is

29Matrices And Determinants

If $$\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]$$ where \(\mathrm{i}=\sqrt{-1}\) and \(\mathrm{B}=\mathrm{A}^{2029}\), then \(\mathrm{B}^{-1}=\)

30Matrices And Determinants

If $$B=\left[\begin{array}{lll}1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3\end{array}\right]$$ is the adjoint of a \(3 \times 3\) matrix A and \(|A|=5\), then \(\alpha\) is equal to

31Matrices And Determinants

If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a \(3 \times 3\) matrix \(\mathrm{A}\) and \(|\mathrm{A}|=4\), then \(\alpha\) is equal to

32Matrices And Determinants

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

33Matrices And Determinants

Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if \(x y z=60\) and \(8 x+4 y+3 z=20\), then \(A\).(adjA)