CUET UG 2025 — Mathematics Algebra

2025mcqeasy

If matrices $A = [1 \quad 2 \quad 3]$ and $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ , then $BA$ is equal to:

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

A
$[14]$
B
$[1 \quad 4 \quad 9]$
C
$\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$
D
$\begin{bmatrix} 1 \\ 4 \\ 9 \end{bmatrix}$

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Solution

Given:

Matrix $A = [1 \quad 2 \quad 3]$ is a row matrix (1×3 matrix)

Matrix $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is a column matrix (3×1 matrix)

For matrix multiplication $BA$ , the number of columns in $B$ equals the number of rows in $A$ (both are 1).

The multiplication is valid and results in a 3×3 matrix.

$BA = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \times [1 \quad 2 \quad 3]$

Each element in $B$ multiplies with the entire row $A$ :

Row 1: $1 \times [1 \quad 2 \quad 3] = [1 \quad 2 \quad 3]$

Row 2: $2 \times [1 \quad 2 \quad 3] = [2 \quad 4 \quad 6]$

Row 3: $3 \times [1 \quad 2 \quad 3] = [3 \quad 6 \quad 9]$

$BA = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$

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Solution

Given:

Matrix $A = [1 \quad 2 \quad 3]$ is a row matrix (1×3 matrix)

Matrix $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is a column matrix (3×1 matrix)

For matrix multiplication $BA$ , the number of columns in $B$ equals the number of rows in $A$ (both are 1).

The multiplication is valid and results in a 3×3 matrix.

$BA = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \times [1 \quad 2 \quad 3]$

Each element in $B$ multiplies with the entire row $A$ :

Row 1: $1 \times [1 \quad 2 \quad 3] = [1 \quad 2 \quad 3]$

Row 2: $2 \times [1 \quad 2 \quad 3] = [2 \quad 4 \quad 6]$

Row 3: $3 \times [1 \quad 2 \quad 3] = [3 \quad 6 \quad 9]$

$BA = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$

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