Algebra

Matrices & Determinants

Easy

core

If matrices $A = [1 \quad 2 \quad 3]$ and $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ , then $BA$ is equal to:

$[14]$

$[1 \quad 4 \quad 9]$

$\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$

$\begin{bmatrix} 1 \\ 4 \\ 9 \end{bmatrix}$

✅ Correct Option: 3

Given:

Matrix $A = [1 \quad 2 \quad 3]$ is a row matrix (1×3 matrix)

Matrix $B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is a column matrix (3×1 matrix)

For matrix multiplication $BA$ , the number of columns in $B$ equals the number of rows in $A$ (both are 1).

The multiplication is valid and results in a 3×3 matrix.

$BA = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \times [1 \quad 2 \quad 3]$

Each element in $B$ multiplies with the entire row $A$ :

Row 1: $1 \times [1 \quad 2 \quad 3] = [1 \quad 2 \quad 3]$

Row 2: $2 \times [1 \quad 2 \quad 3] = [2 \quad 4 \quad 6]$

Row 3: $3 \times [1 \quad 2 \quad 3] = [3 \quad 6 \quad 9]$

$BA = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{bmatrix}$

2022: 16 July Shift 2

The number of all possible matrices of order 3 x 3 with each entry belonging to the set {0, 1} is:

2026: 29 May Shift 1

If $\begin{bmatrix} x-2 & 3 & y \\ -3 & 0 & 2 \\ 4 & z-1 & 0 \end{bmatrix}$ is a skew-symmetric matrix, then the value of $x+y+z$ is:

2023: 22 May Shift 3

Let A = PQ. The elementary operation on A, that produces the same effect as it does on applying on P and keeping Q unchanged is :

(A) $R_i \leftrightarrow R_j$

(B) $R_i \to R_i + KR_j$

(D) $C_i \to C_i + KC_j$

Choose the correct answer from the options given below :

2025: 30 May Shift 2

Which of the following statement('s) is/are TRUE?

(A) Skew symmetric matrix of even order is always symmetric

(B) Skew symmetric matrix of odd order is non-singular

(D) Skew symmetric matrix is always square matrix

Choose the correct answer from the options given below:

2022: 30 Aug Shift 1

If $0 < x < \pi$ and the matrix $\begin{bmatrix} 4\sin x & -1 \\ -3 & \sin x \end{bmatrix}$ is singular, then the values of $x$ are :

2022: 6 Aug Shift 2

If A is a square matrix of order 3 and $|adj A| = 49$ , then $|7A^{-1}|^2$

If matrices A=[123]A = [1 \quad 2 \quad 3]A=[123] and B=[123]B = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}B=​123​​, then BABABA is equal to: