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Matrix Operations Calculator

matrix operations calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

Det 2x2: ad-bc | Det 3x3: cofactor expansion | Inverse: adj(A)/det(A)

Matrix operations on 2x2 and 3x3 matrices. Determinant: ad-bc for 2x2, Sarrus/cofactor for 3x3. Inverse exists only if det โ‰  0. Multiplication: (AB)แตขโฑผ = ฮฃ aแตขโ‚– ร— bโ‚–โฑผ.

Worked Examples

Example 1: 2x2 determinant

Problem:A = [[1,2],[3,4]]

Solution:det = 1ร—4 - 2ร—3 = -2

Result:det(A) = -2

Example 2: 2x2 matrix multiplication

Problem:A = [[1,2],[3,4]], B = [[5,6],[7,8]], find A ร— B

Solution:Row 1: (1ร—5+2ร—7, 1ร—6+2ร—8) = (19, 22). Row 2: (3ร—5+4ร—7, 3ร—6+4ร—8) = (43, 50).

Result:A ร— B = [[19,22],[43,50]]

References

Reviewed by Manoj Kumar, Mathematics Educator ยท Editorial policy