Pertanyaan

Untuk A , B , dan X matriks berordo 2 × 2 . Buktikan bahwa: ( A − 1 ) − 1 = A

Untuk $A$ , $B$ , dan $X$ matriks berordo $2 \times 2$ .

Buktikan bahwa: $(A^{- 1})^{- 1} = A$

A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

$table attributes columnalign right center left columnspacing 0px end attributes row cell Misal space straight A end cell equals cell open parentheses table row straight a straight b row straight c straight d end table close parentheses end cell row cell straight A to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator ad minus bc end fraction open parentheses table row straight d cell negative straight b end cell row cell negative straight c end cell straight a end table close parentheses end cell row cell straight A to the power of negative 1 end exponent end cell equals cell open parentheses table row cell fraction numerator straight d over denominator ad minus bc end fraction end cell cell fraction numerator negative straight b over denominator ad minus bc end fraction end cell row cell fraction numerator negative straight c over denominator ad minus bc end fraction end cell cell fraction numerator straight a over denominator ad minus bc end fraction end cell end table close parentheses end cell row cell open parentheses straight A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 1 over denominator open parentheses fraction numerator straight d over denominator ad minus bc end fraction close parentheses open parentheses fraction numerator straight a over denominator ad minus bc end fraction close parentheses minus open parentheses fraction numerator negative straight c over denominator ad minus bc end fraction close parentheses open parentheses fraction numerator negative straight b over denominator ad minus bc end fraction close parentheses end fraction open parentheses table row cell fraction numerator straight a over denominator ad minus bc end fraction end cell cell fraction numerator straight b over denominator ad minus bc end fraction end cell row cell fraction numerator straight c over denominator ad minus bc end fraction end cell cell fraction numerator straight d over denominator ad minus bc end fraction end cell end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator begin display style ad over open parentheses ad minus bc close parentheses squared end style minus begin display style bc over open parentheses ad minus bc close parentheses squared end style end fraction open parentheses table row cell fraction numerator straight a over denominator ad minus bc end fraction end cell cell fraction numerator straight b over denominator ad minus bc end fraction end cell row cell fraction numerator straight c over denominator ad minus bc end fraction end cell cell fraction numerator straight d over denominator ad minus bc end fraction end cell end table close parentheses end cell row blank equals cell fraction numerator open parentheses ad minus bc close parentheses squared over denominator open parentheses ad minus bc close parentheses end fraction open parentheses table row cell fraction numerator straight a over denominator ad minus bc end fraction end cell cell fraction numerator straight b over denominator ad minus bc end fraction end cell row cell fraction numerator straight c over denominator ad minus bc end fraction end cell cell fraction numerator straight d over denominator ad minus bc end fraction end cell end table close parentheses end cell row blank equals cell fraction numerator open parentheses ad minus bc close parentheses over denominator 1 end fraction open parentheses table row cell fraction numerator straight a over denominator ad minus bc end fraction end cell cell fraction numerator straight b over denominator ad minus bc end fraction end cell row cell fraction numerator straight c over denominator ad minus bc end fraction end cell cell fraction numerator straight d over denominator ad minus bc end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row straight a straight b row straight c straight d end table close parentheses end cell row cell open parentheses straight A to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent end cell equals cell straight A space left parenthesis terbukti right parenthesis end cell row blank blank blank end table$