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To find matrix X such that AX = I, we need to find the inverse of matrix A, i.e., X = A⁻¹.

Mathematics

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To find matrix XX such that AX=IAX = I, we need to find the inverse of matrix AA, i.e., X=A−1X = A^{-1}.

The given matrix AA is:

A=[1243]A = \begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}

  1. Calculate the determinant of matrix AA.

    For a 2×22 \times 2 matrix [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix}, the determinant is ad−bcad - bc.

    det⁡(A)=(1)(3)−(2)(4)=3−8=−5\det(A) = (1)(3) - (2)(4) = 3 - 8 = -5

  2. Find the adjoint of matrix AA.

    For a $2

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