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  "body": "\n## Definition\n\nLet $K$ be a commutative ring, let $A$ be an $m \\times n$ matrix over $K$, and let $1 \\le k \\le \\min(m, n)$.\nA *minor of order $k$* of $A$ is the [[determinant|00KDZRW4C0]] of a $k \\times k$ submatrix of $A$.\nSuch a submatrix consists of the entries in $k$ chosen rows and $k$ chosen columns of $A$.\nFor an $n \\times n$ matrix $A$, delete row $i$ and column $j$ to get an $(n-1) \\times (n-1)$ matrix.\nThe minor $M_{ij}$ is the determinant of this matrix.\n\n## Remarks\n\nThe minors $M_{ij}$ are called *first minors*.\nOver a field, the [[rank|0ZC9YTXZRY]] of $A$ is the largest $k$ such that $A$ has a nonzero minor of order $k$.\nThe minors with the same chosen rows and columns are *principal minors*.\n\n## Explanations\n\n### L1 human\n\nA minor is the determinant of a smaller square piece of a matrix.\nFor a $3 \\times 3$ matrix, we delete one row and one column and take the $2 \\times 2$ determinant of what is left.\nMinors appear in the expansion of determinants and in the formula for the inverse.\n",
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