Question

If A= $open square brackets table row 1 cell space space 2 end cell row 4 cell space space 2 end cell end table close square brackets comma space then space show space that space left enclose 2 space straight A space open vertical bar space equals 4 space close vertical bar space right enclose straight A space end enclose end enclose$

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Solution

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

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