A=1−1121−3111 and 10(B)=422−50α1−23If B is the inverse of A, then find the value α

A=1−1121−3111|A|=1−1121−3111=10adjA=4−5120−2253T=422−5051−23B=A−1=110422−5051−2310(B)=422−5051−23α=5

A=1−1121−3111 and 10(B)=422−50α1−23If B is the inverse of A, then find the value α

A=1−1121−3111|A|=1−1121−3111=10adjA=4−5120−2253T=422−5051−23B=A−1=110422−5051−2310(B)=422−5051−23α=5

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$A = [\begin{array}{l} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{array}]$ and $10 (B) = [\begin{array}{l} 4 & 2 & 2 \\ - 5 & 0 & α \\ 1 & - 2 & 3 \end{array}]$
If $B$ is the inverse of $A$ , then find the value $α$

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$A = [\begin{array}{l} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{array}]$

$| A | = [\begin{array}{l} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{array}] = 10$

$adj A = {[\begin{array}{l} 4 & - 5 & 1 \\ 2 & 0 & - 2 \\ 2 & 5 & 3 \end{array}]}^{T} = [\begin{array}{l} 4 & 2 & 2 \\ - 5 & 0 & 5 \\ 1 & - 2 & 3 \end{array}]$

$B = A^{- 1} = \frac{1}{10} [\begin{array}{l} 4 & 2 & 2 \\ - 5 & 0 & 5 \\ 1 & - 2 & 3 \end{array}]$

$10 (B) = [\begin{array}{l} 4 & 2 & 2 \\ - 5 & 0 & 5 \\ 1 & - 2 & 3 \end{array}]$

$α = 5$

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A=1−1121−3111 and 10(B)=422−50α1−23If B is the inverse of A, then find the value α

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$A = [\begin{array}{l} 1 & - 1 & 1 \\ 2 & 1 & - 3 \\ 1 & 1 & 1 \end{array}]$ and $10 (B) = [\begin{array}{l} 4 & 2 & 2 \\ - 5 & 0 & α \\ 1 & - 2 & 3 \end{array}]$
If $B$ is the inverse of $A$ , then find the value $α$