If and B is a square matrix of order 2 such that AB = I then B = ?

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Inverse of a Matrix

Question

If $A = [\begin{matrix} 3 & - 4 \\ - 1 & 2 \end{matrix}]$ and B is a square matrix of order 2 such that AB = I then B = ?

$[\begin{array}{cc} 1 & 2 \\ 2 & 3 \end{array}]$

$[\begin{array}{cc} 1 & \frac{1}{2} \\ 2 & \frac{3}{2} \end{array}]$

$[\begin{array}{cc} 1 & 2 \\ \frac{1}{2} & \frac{3}{2} \end{array}]$

None of these

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$A = [\begin{array}{cc} 3 & - 4 \\ - 1 & 2 \end{array}] and AB = I \Rightarrow B = I \cdot A^{- 1}$

$∴ [\begin{array}{cc} 3 & - 4 \\ - 1 & 2 \end{array}] [B] = [\begin{array}{ll} 1 0 \\ 0 1 \end{array}] [A^{- 1} = \frac{1}{| A |} [\begin{array}{cc} d & - b \\ - c & a \end{array}]$

$∴ [B] = \frac{1}{2} [\begin{array}{ll} 2 4 \\ 1 3 \end{array}]$

$∴ [B] = [\begin{array}{cc} 1 & 2 \\ \frac{1}{2} & \frac{3}{2} \end{array}]$