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The 12 pages that link to Square matrix, each with the reason it gives.

• DeterminantNarrower topic: Only square matrices have determinants in the standard definition.

• Identity matrixNarrower topic: Identity matrices are square because their diagonal must span equally many rows and columns.

• Matrix exponentialNarrower topic: The matrix exponential is defined for square matrices because its powers must be composable.

• Invertible matrixNarrower topic: Only square matrices have two-sided multiplicative inverses of the same size.

• Cayley–Hamilton theoremNarrower topic: The theorem applies to square matrices because their characteristic polynomials are defined.

• Matrix inverseNarrower topic: Only square matrices have ordinary two-sided inverses.

• Symmetric matrixNarrower topic: Only square matrices can equal their own transpose.

• Diagonal matrixNarrower topic: Having equal dimensions is a prerequisite for the main diagonal and for being diagonal.

• Laplace expansionNarrower topic: Laplace expansion applies to square matrices because only they have determinants.

• Triangular matrixNarrower topic: Triangularity is defined only for square matrices.

• Leibniz formula for determinantsNarrower topic: The formula applies to square arrays of entries.