Algebra

Matrices & Determinants

Easy

core

Let P be a matrix such that $P = \begin{bmatrix} 1 & -1 \\ 0 & 3 \end{bmatrix}$ , then which of the following statements are True?

A. P is a symmetric matrix

B. P is not a skew-symmetric matrix

C. The determinant of P is non-zero

D. P is an invertible matrix

Choose the correct answer from the options given below:

A, B and C only

B, C and D only

A, C and D only

A and D only

✅ Correct Option: 2

Here $P^T=\begin{bmatrix}1 & 0\\ -1 & 3\end{bmatrix} \neq P$ , so P is not symmetric and A fails. Non-zero diagonal entries rule out skew-symmetry, so B is true. Also $|P|=3 \neq 0$ , which makes C true and hence D true as well.

2026: 15 May Shift 1

The matrix $\begin{bmatrix} 2 & -1 & 3 \\ \lambda & 0 & 7 \\ -1 & 1 & 4 \end{bmatrix}$ is not invertible for

2025: 22 May Shift 1

The value(s) of $K$ , for which the system of linear equations $2x + y + z = 1, x + Ky - z = \frac{3}{2}$ and $3y - 5z = 9$ does not possess a unique solution is

2025: 15 May Shift 2

Let $A = [a_{ij}]$ be a square matrix, where $a_{ij} = \begin{cases} 0, & \text{when } i = j \\ 1, & \text{otherwise} \end{cases}$ . If |adj A| = |A|², then which of the following statements 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:

2026: 26 May Shift 2

If A and B are symmetric matrices of the same order then which of the following statements are correct?

A. AB is symmetric matrix

B. AB - BA is skew symmetric matrix

C. $B^TAB$ is symmetric matrix

D. $A - A^T$ is skew symmetric matrix

Choose the correct answer from the options given below:

2025: 13 May Shift 1

If A and B are square matrices of the same order, then (A+B) (A-B) is equal to

2025: 22 May Shift 2

Match List-I with List-II

List-I	List-II
Matrix Product	Order of resultant matrix
---	---
(A) $[a_{ij}]_{2 \times 3} \times [b_{ij}]_{3 \times 4}$	(I) $2 \times 4$
(B) $[a_{ij}]_{2 \times 1} \times [b_{ij}]_{1 \times 3}$	(II) Not possible
(C) $[a_{ij}]_{3 \times 2} \times [b_{ij}]_{3 \times 2}$	(III) $3 \times 3$
(D) $[a_{ij}]_{3 \times 3} \times [b_{ij}]_{3 \times 3}$	(IV) $2 \times 3$

Choose the correct answer from the options given below:

Solution

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