without finding an inverse, can be computed, which is non-zero.

On the other hand, this is a non-invertible matrix:
: This matrix is not invertible, because different vectors and have the same value of , for example, and both give . So it is impossible to reverse the transformation , since different inputs produce the same output. The determinant of is 0, which is a necessary and sufficient condition for a matrix to be non-invertible.

Criteria for invertibility

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