If A is a square matrix, then which of following matrices is not symmetric

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3 and 4 .Determinants and Matrices

easy

If $ A$ is a square matrix, then which of the following matrices is not symmetric

A

$A + A'$

B

$AA'$

C

$A'A$

D

$A - A'$

Solution

(d) Since ${A_{21}} = 1$, so it is symmetric.

$(AA')' = (A')'A' = AA'$, so it is symmetric.

$(A'A)' = A'(A')' = A'A$, so it is symmetric.

But $(A – A')' = A' – A \ne A – A'$. Hence it is not symmetric.

Standard 12

Mathematics

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