If $A equals open square brackets table row 1 2 row 4 2 end table close square brackets$ then show that | 2A | = 4 | A |.

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Solution

straight A equals open square brackets table row 1 2 row 4 2 end table close square brackets therefore space space space open vertical bar straight A close vertical bar equals straight A equals open square brackets table row 1 2 row 4 2 end table close square brackets equals left parenthesis 1 right parenthesis left parenthesis 2 right parenthesis left parenthesis 4 right parenthesis equals 2 minus 8 equals negative 6 space space space space space space space space space 2 straight A equals straight A equals open square brackets table row 2 4 row 4 4 end table close square brackets therefore space space space space space space open vertical bar 2 straight A close vertical bar equals open vertical bar table row 2 4 row 8 4 end table close vertical bar equals 8 minus 32 equals negative 24 equals 4 left parenthesis negative 6 right parenthesis equals 4 space open vertical bar straight A close vertical bar therefore space space space space space space open vertical bar 2 space straight A close vertical bar space equals space 4 space open vertical bar straight A close vertical bar

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