# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [2×2 determinants: the product rule, the scaling rule and the invertibility criterion over ℝ](/en/derivations/derivation-mko-determinant-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-determinant)

For all 2×2 real matrices prove det(AB)=det(A)det(B) and det(tM)=t²det(M), and prove that M is invertible over ℝ exactly when det(M)≠0. With A=[[2,1],[−1,3]] and B=[[1,−2],[4,0]], check the product rule and show AB≠BA; check the scaling rule with t=−3; find A⁻¹ and explain why A, although an integer matrix with det(A)=7≠0, has no integer inverse; use C=[[1,2],[3,4]] (det=−2) to show that a nonzero determinant need not be positive.

Determinants of real 2×2 matrices

derivation-mko-determinant-01





1 1 results · Page 1 of 1