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Show that the matrix M is invertible, and hence, find M⁻¹.

Mathematics

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(d) Show that the matrix MM is invertible, and hence, find M−1M^{-1}.

Given matrix:

M=(3−2574−85−3−4)M = \begin{pmatrix} 3 & -2 & 5 \\ 7 & 4 & -8 \\ 5 & -3 & -4 \end{pmatrix}

Step 1: Calculate the determinant of MM.
A matrix is invertible if and only if its determinant is non-zero.

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