Algebra

Matrices & Determinants

Medium

core

If $A = \begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix}$ and $B^T = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & -1 \end{bmatrix}$ , then $A - B$ is equal to

$\begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 3 & -1 \end{bmatrix}$

$\begin{bmatrix} 3 & 1 \\ -2 & 0 \\ -2 & 1 \end{bmatrix}$

$\begin{bmatrix} 3 & 1 \\ 0 & -2 \\ -2 & 1 \end{bmatrix}$

$\begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix}$

✅ Correct Option: 3

Given $A = \begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix}$ and $B^T = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & -1 \end{bmatrix}$ .

Matrix $A$ is a $3 \times 2$ matrix.

Matrix $B^T$ is a $2 \times 3$ matrix.

To find $B$ , transpose $B^T$ by converting rows to columns.

Row 1 of $B^T$ : $[1, 2, 3]$ becomes Column 1 of $B$

Row 2 of $B^T$ : $[2, 1, -1]$ becomes Column 2 of $B$

$B = \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 3 & -1 \end{bmatrix}$

Both $A$ and $B$ are $3 \times 2$ matrices. Subtract corresponding elements:

$A - B = \begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix} - \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 3 & -1 \end{bmatrix}$

$A - B = \begin{bmatrix} 4-1 & 3-2 \\ 2-2 & -1-1 \\ 1-3 & 0-(-1) \end{bmatrix}$

$A - B = \begin{bmatrix} 3 & 1 \\ 0 & -2 \\ -2 & 1 \end{bmatrix}$

2026: 30 May Shift 2

If A is square matrix of order 3 x 3 such that $a_{ij} = j - i$ , then which of the following statements are correct?

(A) A is a symmetric matrix.

(B) A is a skew symmetric matrix.

(D) A is a diagonal matrix.

Choose the correct answer from the options given below:

2026: 25 May Shift 1

For a square matrix $A$ of order 3, if $\lvert A\rvert = -3$ , then $\lvert 4\,adj A\rvert$ is equal to

2025: 26 May Shift 2

If $A = \begin{bmatrix} x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0 \end{bmatrix}$ is a skew-symmetric matrix, then which of the following are true?

(A) $y > z > x$

(B) $x > y$

(D) $z > x$

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If matrix $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ , then $A^2+I$ is equal to: (Where I is an identity matrix of order 2)

2026: 15 May Shift 1

If $\begin{vmatrix} x-2 & -3 \\ 3x & 2x \end{vmatrix} = 3$ , then the values of $x$ are:

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:

If A=[432−110]A = \begin{bmatrix} 4 & 3 \\ 2 & -1 \\ 1 & 0 \end{bmatrix}A=​421​3−10​​ and BT=[12321−1]B^T = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & -1 \end{bmatrix}BT=[12​21​3−1​], then A−BA - BA−B is equal to