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Maths-

General

Easy

Question

Identify the incorrect statement in respect of two square matrices A and B conformable for sum and product.

t_r(A + B) = t_r(A) + t_r(B)
t_r( $α$ A) = $α$ t_r(A), $α$ $\in$ R
t_r(A^T) = t_r(A)
t_r(AB) ≠ t_r(BA)

hint Hint:

check whether the properties of matrices match with those given in the options. you can also assume a matrix and do the operations and then verify whether the properties are correct.

The correct answer is: t_r(AB) ≠ t_r(BA)

tr(AB) ≠ tr(BA)

tr( A+ B) = tr(A) + tr(B )
tr(aA) = a x tr(A), a c R
tr(A^T) = tr(A)
tr( AB)= tr(BA)
these properties are correct.

trace of a matrix is the sum of the diagonal elements of a matrix.

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