Question
(adj AT) – (adj A)T equals-
- 2 |A|
- 2 |A| I
- zero matrix
- Unit matrix
The correct answer is: zero matrix
we are asked to solve ![left parenthesis a d j space A to the power of T right parenthesis space – space left parenthesis a d j space A right parenthesis to the power of T space](data:image/png;base64,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)
![space a d j A to the power of T space space minus left parenthesis a d j A right parenthesis to the power of T space space space space space
equals ∣ A to the power of T space ∣ left parenthesis A to the power of T space right parenthesis to the power of negative 1 end exponent minus left parenthesis ∣ A ∣ A to the power of negative 1 end exponent space right parenthesis to the power of T space space
equals ∣ A ∣ to the power of T space space left parenthesis A to the power of negative 1 end exponent space right parenthesis to the power of T minus left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T space space ∣ A ∣ to the power of T space space
space equals ∣ A ∣ to the power of T space left parenthesis left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T minus left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T right parenthesis space space
space equals O](data:image/png;base64,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)
Therefore the correct option is zero matrix
Related Questions to study
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