If $A^{- 1} = ⎣ ⎡ 3 - 15 5 - 1 6 - 2 1 - 5 2 ⎦ ⎤, B = ⎣ ⎡ 1 - 1 0 23 - 2 - 2 01 ⎦ ⎤$ find $(A B)^{- 1}$

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A^{- 1} = ⎣ ⎡ 3 - 15 5 - 1 6 - 2 1 - 5 2 ⎦ ⎤, B = ⎣ ⎡ 1 - 1 0 23 - 2 - 2 01 ⎦ ⎤

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(A B)^{- 1}

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Text solutionVerified

(A B)^{- 1} = B^{- 1} A^{- 1}

∣ B ∣ = (1 \times 3) + 1 \times (2 - 4) = 1 \neq = 0

co factor

B = ⎣ ⎡ 312212625 ⎦ ⎤

(A B)^{- 1} = B^{- 1} A^{- 1}

= ⎣ ⎡ 312212625 ⎦ ⎤ ⎣ ⎡ 3 - 15 5 - 1 6 - 2 1 - 5 + 2 ⎦ ⎤ = ⎣ ⎡ 9 - 2 1 - 3 10 502 ⎦ ⎤

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