<s>[INST] Linear Algebra matrix calculation help please A = $$
    \begin{pmatrix}
    2 & 1 \\
    3 & 4 \\
    \end{pmatrix}
$$
How can i find matrix B s.t B^3 = A?
 [/INST] You can define $B$ as
$$B = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
And solve the equation following equation system:
$$B^3 = \begin{bmatrix} a & b \\ c & d \end{bmatrix}*\begin{bmatrix} a & b \\ c & d \end{bmatrix}*\begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix},$$
what equals to
$$\begin{bmatrix} a^3+2abc+bdc & a^2b+b^2c+abd+bd^2 \\ a^2c+acd+c^2d+d^2c & abc+2bcd+d^3 \end{bmatrix} = \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$$
And solving that 4 equation system will give you the solution.
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