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Let {A}{d}{n}{B} be {3}{3} matrtices of ral numbers, where {A}

Question

Let $A d n B$ be $3 \times 3$ matrtices of ral numbers, where $A$ is symmetric, $B$ is skew-symmetric , and $(A + B) (A - B) = (A - B) (A + B) ˙$ If $(A B)^{t} = (- 1)^{k} A B, w h e r e (A B)^{t}$ is the transpose of the mattix $A B,$ then find the possible values of $k ˙$

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Emily Discussed

Let

A d n B

3 \times 3

matrtices of ral numbers, where

A

is symmetric,

B

is skew-symmetric , and

(A + B) (A - B) = (A - B) (A + B) ˙

(A B)^{t} = (- 1)^{k} A B, w h e r e (A B)^{t}

is the transpose of the mattix

A B,

then find the possible values of

k ˙

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Question Text

Let

A d n B

3 \times 3

matrtices of ral numbers, where

A

is symmetric,

B

is skew-symmetric , and

(A + B) (A - B) = (A - B) (A + B) ˙

(A B)^{t} = (- 1)^{k} A B, w h e r e (A B)^{t}

is the transpose of the mattix

A B,

then find the possible values of

k ˙

Filo tutor solution