Definition of Matrix Inverse
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If $AB = I$ then $BA = I$
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Inverting non positive definite covariance matrix
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Proof that the inverse of a square matrix is unique
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Deriving the inverse of a 2x2 matrix
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An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
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Invertibility of the Product of Two Matrices
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Inverse of the sum of matrices
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Linear Transformation and Matrices
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Why is inverse of orthogonal matrix is its transpose?
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Matrix with zeros on diagonal and ones in other places is invertible
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Solving the matrix equation and finding the matrices inverse
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For a square matrix $A$ presence of $n$ linearly independent eigenvectors implies full rank, thereby invertible?
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Characteristic polynomial of an inverse
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Determinant of the inverse matrix
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Inverse of an invertible triangular matrix (either upper or lower) is triangular of the same kind
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Is inverse matrix convex?
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Product of a primitive matrix and its transpose.