Algebra

Matrices & Determinants

Easy

core

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is

$\begin{bmatrix}\frac{1}{x} & 0 & 0 \\ 0 & \frac{1}{y} & 0 \\ 0 & 0 & \frac{1}{z}\end{bmatrix}$

$\begin{bmatrix}\frac{1}{yz} & 0 & 0 \\ 0 & \frac{1}{xz} & 0 \\ 0 & 0 & \frac{1}{xy}\end{bmatrix}$

$\begin{bmatrix}\frac{1}{x^2yz} & 0 & 0 \\ 0 & \frac{1}{xy^2z} & 0 \\ 0 & 0 & \frac{1}{xyz^2}\end{bmatrix}$

$\begin{bmatrix}\frac{1}{xyz} & 0 & 0 \\ 0 & \frac{1}{xyz} & 0 \\ 0 & 0 & \frac{1}{xyz}\end{bmatrix}$

✅ Correct Option: 1

Given matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ where $x, y, z$ are non-zero numbers.

This is a diagonal matrix, where all elements are zero except those on the main diagonal.

For diagonal matrices, the inverse is obtained by taking the reciprocal of each diagonal element.

The inverse $A^{-1}$ is:

$A^{-1} = \begin{bmatrix}\frac{1}{x} & 0 & 0 \\ 0 & \frac{1}{y} & 0 \\ 0 & 0 & \frac{1}{z}\end{bmatrix}$

2023: 23 May Shift 3

The inverse of the matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ is:

2025: 3 June Shift 1

Which of the following statements are correct?

(A) Inverse of a matrix, if it exists, is unique

(B) $(kA)' = -kA'$ (where k is any real number)

(D) For an invertible matrix $A$ , $(A')^{-1} = (A^{-1})'$

Choose the correct answer from the options given below:

2026: 30 May Shift 2

If A and B are invertible matrices of the same order, then

Match List-I with List-II

List-I (Determinant)	List-II (Equal to)
(A) $\left\vert A^{-1}B \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert \left\vert B \right\vert}$
(B) $\left\vert AB^{-1} \right\vert$	(II) $\dfrac{\left\vert B \right\vert}{\left\vert A \right\vert}$
(C) $\left\vert A^{-1}B^{-1} \right\vert$	(III) $\left\vert A \right\vert \left\vert B \right\vert$
(D) $\left\vert AB \right\vert$	(IV) $\dfrac{\left\vert A \right\vert}{\left\vert B \right\vert}$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

If $x, y$ and $z$ are real number such that $x + y + z = 0$ , then value of $\begin{vmatrix}3x & -x+y & -x+z\\x-y & 3y & z-y\\x-z & y-z & 3z\end{vmatrix}$ is

2025: 13 May Shift 2

Let $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$ . Then

(A) $x = -4$

(B) $x = -6$

(D) $x = 6$

Choose the correct answer from the options given below:

2025: 15 May Shift 2

If A and B are two square symmetric matrices of same order, then AB-BA is

If x,y,zx, y, zx,y,z are non-zero numbers, then the inverse of matrix A=[x000y000z]A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}A=​x00​0y0​00z​​ is

Solution

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Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $x, y, z$ are non-zero numbers, then the inverse of matrix $A = \begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}$ is