Algebra

Matrices & Determinants

Medium

core

If A and B are two square symmetric matrices of same order, then AB-BA is

a symmetric matrix

a skew-symmetric matrix

neither a symmetric nor a skew-symmetric

always a diagonal matrix

✅ Correct Option: 2

A and B are square symmetric matrices of the same order.

For a symmetric matrix, $A^T = A$ (the matrix equals its own transpose).

Since A and B are symmetric:

$A^T = A$

$B^T = B$

Let $P = AB - BA$

Taking the transpose:

$P^T = (AB - BA)^T$

$P^T = (AB)^T - (BA)^T$

Using the transpose property $(XY)^T = Y^T X^T$ :

$P^T = B^T A^T - A^T B^T$

Substituting $A^T = A$ and $B^T = B$ :

$P^T = BA - AB$

$P^T = -(AB - BA)$

$P^T = -P$

A matrix M is skew-symmetric when $M^T = -M$ .

Since $P^T = -P$ , the matrix $(AB - BA)$ is a skew-symmetric matrix.

2026: 30 May Shift 2

If $A = \begin{bmatrix}\cos\alpha & \sin\alpha\\-\sin\alpha & \cos\alpha\end{bmatrix}$ , then the value of $1000|A^n| + 2|A|$ for a positive integer $n$ , is equal to

2026: 18 May Shift 1

If $\begin{vmatrix}6 & 7\\ 3 & 8\end{vmatrix} = \begin{vmatrix}3x & 6\\ -1 & x\end{vmatrix}$ , then the sum of values of $x$ is equal

2026: 19 May Shift 2

The value of $\begin{vmatrix} \log_3 512 & \log_4 3 \\ \log_3 8 & \log_4 9 \end{vmatrix}$ is:

2026: 19 May Shift 2

If $\begin{vmatrix} 1+x^2 & 1 & 1 \\ 1 & 1+y^2 & 1 \\ 1 & 1 & 1+z^2 \end{vmatrix} = k\left(1 + \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$ then $k$ is equal to

2025: 2 June Shift 1

The matrix $A = \begin{bmatrix}0 & 0 & 5\\0 & 5 & 0\\5 & 0 & 0\end{bmatrix}$ is a

(A) Diagonal matrix

(B) Scalar matrix

(D) Symmetric matrix

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

If the system of linear equations

$x + 2y - 3z = 1$

$(2p+1)y + z = 2$

$3x + 3z = 5$

has a unique solution, then p can not be equal to

If A and B are two square symmetric matrices of same order, then AB-BA is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)