Algebra

Matrices & Determinants

Easy

applied

Match the LIST-I with LIST-II

LIST-I LIST-II
A. Column matrix I. $\begin{bmatrix}1 & 2 & 3\end{bmatrix}$
B. Row matrix II. $\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
C. Diagonal matrix III. $\begin{bmatrix}1\\ 2\\ 3\end{bmatrix}$
D. Scalar matrix IV. $\begin{bmatrix}2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$

Choose the correct answer from the options given below:

	LIST-I		LIST-II
A.	Column matrix	I.	$\begin{bmatrix}1 & 2 & 3\end{bmatrix}$
B.	Row matrix	II.	$\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}$
C.	Diagonal matrix	III.	$\begin{bmatrix}1\\ 2\\ 3\end{bmatrix}$
D.	Scalar matrix	IV.	$\begin{bmatrix}2 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 2\end{bmatrix}$

A-III, B-II, C-IV, D-I

A-III, B-IV, C-I, D-II

A-III, B-I, C-II, D-IV

A-III, B-II, C-I, D-IV

✅ Correct Option: 3

A column matrix has a single column, matching III.

A row matrix has a single row, matching I.

A diagonal matrix has non-zero entries only on the main diagonal, matching II.

A scalar matrix is a diagonal matrix with all diagonal entries equal, matching IV.

2025: 15 May Shift 2

If $A = [a_{ij}]$ be square matrix of order 3, such that $a_{ij} = i + j$ , $\forall i, j$ then which of the following are correct?

(A) A is a skew-symmetric matrix.

(B) A is a non-singular matrix.

(D) A is a symmetric matrix.

Choose the correct answer from the options given below:

2025: 26 May Shift 2

Match List-I with List-II

List-I	List-II
Matrix/equations	Values
(A) $\begin{bmatrix} 2x+1 & 3y \\ 0 & y^2-5y \end{bmatrix} = \begin{bmatrix} x+3 & y^2+2 \\ 0 & -6 \end{bmatrix}$	(I) $x = 2, y = -1$
(B) $\begin{bmatrix} 1 & 2 & -1 \\ x & 0 & 3 \\ y & 3 & 4 \end{bmatrix}$ is symmetric	(II) $x = 2, y = 2$
(C) $[x \ \ 1]\begin{bmatrix} 1 & 0 \\ -2 & -3 \end{bmatrix}\begin{bmatrix} 5 & 2 \\ 0 & y \end{bmatrix} = O$	(III) $x = -2, y = 2$
(D) $\begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix}\begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ -1 & y/2 \end{bmatrix}$	(IV) $x = 2, y = 0$

Choose the correct answer from the options given below:

2026: 29 May Shift 1

Let $A = \begin{bmatrix} 1 & -3 \\ 1 & 2 \end{bmatrix}$ , $B = \begin{bmatrix} 4 & 6 \\ -2 & 2 \end{bmatrix}$ and $C$ be a matrix such that $C = AB$ . Then $|(BC)^{-1}|$ is equal to

2026: 18 May Shift 1

If a matrix has 7 elements, then it can be a

(A) Scalar matrix

(B) Symmetric matrix

(D) Row matrix

Choose the correct answer from the options given below:

2023: 22 May Shift 3

Which of the following statements is incorrect regarding matrices ?

For any matrices A and B of suitable orders,

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:

Solution

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