Let A = $open square brackets table row 5 cell 5 straight alpha end cell straight alpha row 0 straight alpha cell 5 straight alpha end cell row 0 0 5 end table close square brackets$ If |A²| = 25, then |α| equals

5²

1

1/5

5

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Solution

1/5

straight A squared space equals space open square brackets table row 5 cell 5 straight alpha end cell straight alpha row 0 straight alpha cell 5 straight alpha end cell row 0 0 5 end table close square brackets open square brackets table row 5 cell 5 straight alpha end cell straight alpha row 0 straight alpha cell 5 straight alpha end cell row 0 0 5 end table close square brackets straight A squared space equals space open square brackets table row 25 cell 25 straight alpha plus 5 straight alpha squared end cell cell 5 straight alpha end cell row 0 cell straight alpha squared end cell cell 5 straight alpha squared plus 25 straight alpha end cell row 0 0 25 end table close square brackets 625 space straight alpha squared space equals space 25 rightwards double arrow space vertical line straight alpha vertical line space equals space 1 fifth

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