Maths-

General

Easy

Question

# If is symmetric then trace of A is

- 5
- -10
- 10
- 15

Hint:

### A square matrix B which of size n × n is considered to be symmetric if and only if B^{T} = B. Consider the given matrix B, that is, a square matrix that is equal to the transposed form of that matrix, called a symmetric matrix.

This can be represented as: If B = [bij]n×n is the symmetric matrix, then bij = for all i and j or 1 ≤ i ≤ n, and 1 ≤ j ≤ n. Here,

- n is any natural number.
- bi is an element at position (i, j) which is i
^{th} row and j^{th }column in matrix B and
- bji is an element at position (j, i) which is j
^{th} row and i^{th} column in matrix B.

^{th}row and j^{th }column in matrix B and^{th}row and i^{th}column in matrix B.## The correct answer is: 10

### Given is symmetric.

Thus, trace of A is 10.

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