CUET UG 2025 — Mathematics Algebra

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The inverse of the matrix $A = \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$ is

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
$\frac{1}{64} \begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$
B
$\frac{1}{64} \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$
C
$\begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$
D
$\frac{1}{64} \begin{bmatrix} \frac{1}{32} & 0 & 0 \\ 0 & \frac{1}{16} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$

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Solution

Matrix $A$ is a diagonal matrix:

$A = \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$

All non-diagonal entries are zero, with non-zero elements only on the main diagonal.

For a diagonal matrix, the inverse is found by taking the reciprocal of each diagonal element.

$\frac{1}{\frac{1}{2}} = 2$

$\frac{1}{\frac{1}{4}} = 4$

$\frac{1}{\frac{1}{8}} = 8$

The inverse matrix is:

$A^{-1} = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$

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Options

$\frac{1}{64} \begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$

$\frac{1}{64} \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$

$\begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$

$\frac{1}{64} \begin{bmatrix} \frac{1}{32} & 0 & 0 \\ 0 & \frac{1}{16} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$

Solution

Matrix $A$ is a diagonal matrix:

$A = \begin{bmatrix} \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{8} \end{bmatrix}$

All non-diagonal entries are zero, with non-zero elements only on the main diagonal.

For a diagonal matrix, the inverse is found by taking the reciprocal of each diagonal element.

$\frac{1}{\frac{1}{2}} = 2$

$\frac{1}{\frac{1}{4}} = 4$

$\frac{1}{\frac{1}{8}} = 8$

The inverse matrix is:

$A^{-1} = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 8 \end{bmatrix}$

CUET UG 2025 — Mathematics Algebra

Options

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Solution

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CUET UG Algebra in other years

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CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra