(B) For the matrix multiplication $AB = C$ to be defined,the number of columns in matrix $A$ must be equal to the number of rows in matrix $B$. If $A$

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$A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$

(B) For the matrix multiplication $AB = C$ to be defined,the number of columns in matrix $A$ must be equal to the number of rows in matrix $B$. If $A$ is an $m \times n$ matrix and $B$ is an $n \times p$ matrix,then the resulting matrix $C$ will have the dimensions $m \times p$. Looking at option $B$: If $A$ is $3 \times 2$ and $B$ is $2 \times 3$,then $C$ must be a $3 \times 3$ matrix. Therefore,the correct dimensions are $A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

Easy

If $AB = C$,then the dimensions of matrices $A, B, C$ are:

A
$A_{2 \times 3}, B_{3 \times 2}, C_{2 \times 2}$
B
$A_{3 \times 2}, B_{2 \times 3}, C_{3 \times 3}$
C
$A_{3 \times 3}, B_{2 \times 3}, C_{3 \times 3}$
D
$A_{3 \times 2}, B_{2 \times 3}, C_{2 \times 2}$

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3 and 4 .Determinants and Matrices

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Types of matrices, Algebra of matrices

Let $S = \left\{ \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} : a_{ij} \in \{0, 1, 2\}, a_{11} = a_{22} \right\}$. Then the number of non-singular matrices in the set $S$ is

DifficultJEE MAIN 2013

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If $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & 3 & -1 \\ 3 & 1 & 2 \end{bmatrix}$ and $I$ is a unit matrix of $3^{rd}$ order,then $(A^2 + 9I)$ equals

Easy

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If matrix $A = \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$,then the value of $\prod_{k=1}^{36} \begin{bmatrix} 1 & 3k + \frac{1}{3} \\ 0 & 1 \end{bmatrix}$ is equal to :-

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If $A$ and $B$ are square matrices of size $n \times n$ such that $A^2 - B^2 = (A - B)(A + B)$,then which of the following will be always true?

EasyAIEEE 2006

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$G = \left\{ \begin{bmatrix} x & x \\ x & x \end{bmatrix} : x \in \mathbb{R} \setminus \{0\} \right\}$ is a group with respect to matrix multiplication. In this group,the inverse of $\begin{bmatrix} 1/3 & 1/3 \\ 1/3 & 1/3 \end{bmatrix}$ is

MediumKCET 2011

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If $AB = C$,then the dimensions of matrices $A, B, C$ are:

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Let $S = \left\{ \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} : a_{ij} \in \{0, 1, 2\}, a_{11} = a_{22} \right\}$. Then the number of non-singular matrices in the set $S$ is

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