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Exercise 2

Avg difficulty 2.5

If A=(1−231)andB=(41−1−2),A = \begin{pmatrix} 1 & -2 \\ 3 & 1 \end{pmatrix} \quad \text{and} \quad B = \begin{pmatrix} 4 & 1 \\ -1 & -2 \end{pmatrix}, find each of the following.

  1. A+BA + B

  2. 2A−3B2A - 3B

  3. ABAB

  4. BABA

  5. A−1A^{-1}

  6. B−1B^{-1}

Judson, The ODE Project, §3.1 Linear Algebra in a Nutshell, Exercise 2

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Adapted from The ODE Project © 2019–2025 Thomas W. Judson. Licensed under CC BY 4.0. Source: The ODE Project. Imported at revision 7935458.