If , then A–1 is given by?

Engineering

Mathematics

Introduction to Matrix

Inverse of a Matrix

Question

If $A [\begin{array}{cc} 1 & 1 \\ 2 & 0 \end{array}] = [\begin{array}{cc} 3 & 2 \\ 1 & 1 \end{array}]$ , then A^–1 is given by?

$[\begin{array}{cc} 0 & - 1 \\ - 2 & - 4 \end{array}]$

$[\begin{array}{cc} 0 & 1 \\ 2 & - 4 \end{array}]$

None of these

$[\begin{array}{cc} 0 & - 1 \\ 2 & - 4 \end{array}]$

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Let $A = [\begin{array}{ll} a b \\ c d \end{array}]$

$[\begin{array}{ll} a b \\ c d \end{array}] [\begin{array}{ll} 1 1 \\ 2 0 \end{array}] = [\begin{array}{ll} 3 2 \\ 1 1 \end{array}]$

$[\begin{array}{ll} a + 2 b a \\ c + 2 d c \end{array}] = [\begin{array}{ll} 3 2 \\ 1 1 \end{array}]$

comparing a = 2, c = 1

a + 2b = 3

b = 1/2

c + 2d = 1

$∴ A = [\begin{array}{ll} 2 1 / 2 \\ 1 0 \end{array}]; | A | = 0 - 1 / 2 = - 1 / 2$

$A^{- 1} = \frac{adj A}{| A |} = - 2 [\begin{array}{cc} 0 & - 1 / 2 \\ - 1 & 2 \end{array}]$

$A^{- 1} = [\begin{array}{cc} 0 & 1 \\ 2 & - 4 \end{array}]$