18/3848–12FE Reference Handbook 10.6 · Mathematics · p. 59 Inverse adj(A)/|A|; p. 60 second-order determinant
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Handbook formula

2×2 Determinant and Inverse

p. 59 prints A^{−1} = adj(A)/|A|. p. 60 prints the second-order determinant ad − bc and says a matrix is nonsingular iff the determinant is not zero. The compact 2×2 inverse matrix below is that definition expanded; it is not a separate printed template. Matrix multiplication is not commutative (p. 59).

Entries
Determinant

Step-by-step solved example

A=[[2,1],[0,4]]. Find det A and A inverse.

A =2 10 4A⁻¹ = (1/8)4 −10 2Replay
2×2 linear map sends basis vectors; det is the parallelogram area.

  1. 1. Determinant

    ad−bc=8−0=8.

  2. 2. Inverse

    (1/8)[[4,−1],[0,2]].

Answer: det=8; A^{-1}=(1/8)[[4,−1],[0,2]]

10 practice questions

0/10 correct

1.det[[3,1],[2,4]] =

2.A is singular when

3.Cramer’s x = det(Ax)/det(A) replaces

4.det(kA) for 2×2 equals

5.Inverse of [[1,0],[0,2]] is

6.det(AB)=

7.Trace of [[4,1],[2,3]] is

8.Solving Ax=b with A^{-1} is

9.det[[0,1],[1,0]] =

10.A 2×2 rotation matrix has det