Algebra

Matrices & Determinants

Medium

common

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:

2 × 4

4 × 2

3 × 4

4 × 3

✅ Correct Option: 2

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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If a matrix $A = \begin{bmatrix} x+3 & 3 \\ 2x+1 & 5 \end{bmatrix}$ is singular , then the value of $x$ will be

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Let $A=[a_{ij}]$ be a matrix of order $3 \times 4$ such that $a_{ij}=\begin{cases}2i-3j, & i \ge j \\ 3i+j, & i<j\end{cases}$ then the sum of all the elements of the first two rows of this matrix is:

2022: 25 May Shift 1

If $A = \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and B is a square matrix of order 3, then |AB| is equal to:

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For the matrix $A = \begin{bmatrix} 2 & -1 & -1 \\ 0 & 2 & 3 \\ 1 & -2 & 1 \end{bmatrix}$ , which of the following statements are correct?

(A) The order of the matrix is 3 × 3

(B) |A| = 21

(D) A is skew symmetric matrix

Choose the correct answer from the options given below:

2025: 27 May Shift 1

If A and B are symmetric matrices of the same order, then which of the following are true?

(A) AB - BA is a skew symmetric matrix

(B) AB is a symmetric matrix

(D) AB + BA is a symmetric matrix

Choose the correct answer from the options given below:

2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
(A) A square matrix $P$ is said to be non-singular if	(I) $\vert P\vert = 0$
(B) A square matrix $P$ is said to be singular if	(II) $P P^T$ is symmetric
(C) If a matrix $P$ is both symmetric and skew-symmetric, then	(III) $\vert P\vert \neq 0$
(D) If $P$ is a square matrix, then	(IV) $P$ is a null matrix

Choose the correct answer from the options given below:

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

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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: