CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Let $A = [a_{ij}]_{3×2}$ and $B = [b_{ij}]_{3×4}$ be two matrices. Then the order of the matrix $(A^T . B)^T$ is:

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
2 × 4
B
4 × 2
C
3 × 4
D
4 × 3

Did you get this right?

Solution

Given matrix $A$ has order $3×2$ (3 rows and 2 columns) and matrix $B$ has order $3×4$ (3 rows and 4 columns).

When a matrix is transposed, rows become columns and columns become rows. If a matrix is $m×n$ , its transpose is $n×m$ .

For matrix multiplication $X \cdot Y$ to be possible, the number of columns in $X$ must equal the number of rows in $Y$ . The resulting matrix has order (rows of $X$ ) × (columns of $Y$ ).

Since $A$ is $3×2$ , applying transpose:

$A^T$ is $2×3$

To multiply $A^T \cdot B$ :

$A^T$ is $2×3$ and $B$ is $3×4$

Columns in $A^T$ = 3 and rows in $B$ = 3, so multiplication is possible.

$A^T \cdot B$ is $2×4$

Since $A^T \cdot B$ is $2×4$ , applying transpose:

$(A^T \cdot B)^T$ is $4×2$

Therefore, the order of $(A^T \cdot B)^T$ is $4×2$ .

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CUET UG Algebra in other years

Algebra 2026 Algebra 2024 Algebra 2023 Algebra 2022

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Work through every CUET UG Algebra PYQ, year by year.

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CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Let $A = [a_{ij}]_{3×2}$ and $B = [b_{ij}]_{3×4}$ be two matrices. Then the order of the matrix $(A^T . B)^T$ is:

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
2 × 4
B
4 × 2
C
3 × 4
D
4 × 3

Did you get this right?

Solution

Given matrix $A$ has order $3×2$ (3 rows and 2 columns) and matrix $B$ has order $3×4$ (3 rows and 4 columns).

When a matrix is transposed, rows become columns and columns become rows. If a matrix is $m×n$ , its transpose is $n×m$ .

For matrix multiplication $X \cdot Y$ to be possible, the number of columns in $X$ must equal the number of rows in $Y$ . The resulting matrix has order (rows of $X$ ) × (columns of $Y$ ).

Since $A$ is $3×2$ , applying transpose:

$A^T$ is $2×3$

To multiply $A^T \cdot B$ :

$A^T$ is $2×3$ and $B$ is $3×4$

Columns in $A^T$ = 3 and rows in $B$ = 3, so multiplication is possible.

$A^T \cdot B$ is $2×4$

Since $A^T \cdot B$ is $2×4$ , applying transpose:

$(A^T \cdot B)^T$ is $4×2$

Therefore, the order of $(A^T \cdot B)^T$ is $4×2$ .

Your note

CUET UG Algebra in other years

Algebra 2026 Algebra 2024 Algebra 2023 Algebra 2022

Keep practicing Algebra

Work through every CUET UG Algebra PYQ, year by year.

Browse all Mathematics topics

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

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