Read the two statements and choose the correct option.
I. If $A$ and $B$ are symmetric matrices of the same order, $AB - BA$ is skew-symmetric.
II. If $A$ and $B$ are symmetric matrices of the same order, $AB$ is always symmetric.

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$(AB - BA)' = B'A' - A'B' = BA - AB$ , so I is true.
$(AB)' = B'A' = BA$ , which equals $AB$ only when $A$ and $B$ commute, so II is false.

Ten questions from Matrices, at your own pace.

Read the two statements and choose the correct option.I. If AAA and BBB are symmetric matrices of the same order, AB−BAAB - BAAB−BA is skew-symmetric.II. If AAA and BBB are symmetric matrices of the same order, ABABAB is always symmetric.