Jadyn V. Breland
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Problem Solving
This page is dedicated to problems that I really enjoyed. Click on the links to view my solutions. Send me an email if you find a mistake!
How many \(2 \times 2\) matrices \(A \in \text{Mat}_{2\times 2}(\mathbb{F}_p)\) satisfy \(A^2 = A\)?
Let \(p\) be a prime and \(F = \mathbb{F}_p\) the field with \(p\) elements, and \(V = F^4\) the standard \(F\)-vector space of dimension \(4\). Count the number of \(F\)-linear subspaces of \(V\).