Question

Which of the following is not true?

Addition of multiplication is commutative
AB-BA is always a skew-symmetric matrix for symmetric matrices A and B
AB+BA is always a skew-symmetric matrix for symmetric matrices A and B
Multiplication of matrices in not commutative in general

Answer 1

Answer:

Atomicity is defined as the total number of atoms present in a molecule. For example, each molecule of oxygen is composed of two oxygen atoms. So atomicity of oxygen is 2.In older contexts, the term atomicity is sometimes used in the same sense as valency.

Answer 2

AB+BA is always a skew-symmetric matrix for symmetric matrices A and B

Given:

A and B are symmetric matrices.

To Find:

AB + BA is not a skew-symmetric matrix.

Solution:

we know, A and B are symmetric matrices so

  A' = A   and B' = B ---------> 1

now,

(AB + BA)' = (AB)' + (BA)'

                 = B'A' + A'B'

                 = BA + AB        ( From 1)

                 $\neq -(BA + AB)$

Hence, AB+BA is always a skew-symmetric matrix for symmetric matrices A and B is not true.

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