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:''AB'' = ''BA'' = I (I: [[identity matrix]])
:''AB'' = ''BA'' = I (I: [[identity matrix]])
A matrix is invertible if and only if it has a nonzero determinant. Only square matrices (''n'' x ''n'') are invertible.
A matrix is invertible if and only if it has a nonzero [[determinant]]. Only square matrices (''n'' x ''n'') are invertible.
It can be shown that, for any invertible matrix ''A'', there is only one matrix ''B'' such that ''AB'' = I; this unique matrix is called the [[inverse matrix]] of ''A'', and represented as ''A<sup>-1</sup>''.
It can be shown that, for any invertible matrix ''A'', there is only one matrix ''B'' such that ''AB'' = I; this unique matrix is called the [[inverse matrix]] of ''A'', and represented as ''A<sup>-1</sup>''.