Find the matrix A

A $\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix}$ = $\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}$

$\begin {bmatrix} 2 & 1\\-^1/_2 & -^1/_2 \end {bmatrix}$

$\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}$

$\begin {bmatrix} 2 & 1\\0 & -1 \end {bmatrix}$

$\begin {bmatrix} 2 & 1\\^1/_2 & -2 \end {bmatrix}$

Correct answer is B

Let A = $\begin {bmatrix} a & b\\ c & d \end {bmatrix}$

i.e $\begin{bmatrix} a & b\\c & d \end{bmatrix}$ $\begin{bmatrix} 0 & 1\\2 & -1 \end{bmatrix}$ = $\begin{bmatrix} 2 & -1\\1 & 0 \end{bmatrix}$

$\implies \begin {bmatrix} a(0) + b(2) & a(1) + b(-1)\\ c(0) + d(2) & c(1) + d(-1)\end {bmatrix}$ = $\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}$

$\implies \begin {bmatrix} 2b & a - b\\2d & c - d\end {bmatrix}$ = $\begin {bmatrix} 2 & -1\\ 1 & 0 \end {bmatrix}$

By comparing

2b = 2

a - b = -1

2d = 1 and

c - d = 0

∴ b = $^2/_2$ = 1

a - b = -1

⇒ a - 1 = -1

∴ a = 0

∴ d = $^1/_2$

⇒ c = d

∴ c = $^1/_2$

∴The matrice A = $\begin {bmatrix} 0 & 1\\^1/_2 & ^1/_2 \end {bmatrix}$

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Find the matrix A A [012−1]\begin {bmatrix} 0 & 1\\2 & -1 \end {bmatrix} = [2−110]\begin {bmatrix} 2 & -1\\1 & 0 \end {bmatrix}