http://mathworld.wolfram.com/CongruentMatrices.html

Two square matrices  and  are called congruent if there exists a nonsingular matrix  such that

where  is the transpose.

Congruent

Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.

Note: Congruent segments, sides, and angles are often marked.

Congruent Segments Congruent Angles

      
All four sides of this rhombus are marked to show they are congruent to each other.

The marked angles of this isosceles triangle are congruent to each other.

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