If A and B are symmetric matrices of the same order, then A B-B A is a : Option 1: symmetric matrix Option 2: zero matrix Option 3: skew symmetric matrix Option 4: identity matrix

The answer is 'skew symmetric matrix'. View full solution:

Algebra > Matrices & Determinants

Easy

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If $A$ and $B$ are symmetric matrices of the same order, then $A B-B A$ is a :

symmetric matrix

zero matrix

skew symmetric matrix

identity matrix

✅ Correct Option: 3

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Match List-I with List-II

List-I	List-II
Type of matrix	Conditions
(A) Square matrix A	(I) $A = [a_{ij}]_{m \times m}$ where $\begin{cases} a_{ij} = 0 & , i \neq j \\ a_{ij} = k & , i = j \end{cases}$ , where $k \neq 0$ is constant.
(B) Scalar Matrix A	(II) $A = [a_{ij}]_{m \times m}$
(C) Diagonal matrix A	(III) $A = [a_{ij}]_{m \times m}$ where $\begin{cases} a_{ij} = 0 & , i \neq j \\ a_{ij} = 1 & , i = j \end{cases}$
(D) Identity matrix A	(IV) $A = [a_{ij}]_{m \times m}$ where $a_{ij} = 0$ , $i \neq j$

Choose the correct answer from the options given below:

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Let the matrix $A = [a_{ij}]_{3\times3}$ be defined by

$a_{ij} = \begin{cases} 2i + 3j, & i < j \\ 5, & i = j \\ 3i - 2j, & i > j \end{cases}$

The number of elements in the matrix A which are greater than 7, is: