ALG1_T1

2024-09-02
1834

Problems

find the number of elements in $G L_{2} (F_{p})$ . << this is the set of all nxxn matrices.
Show that $A B - B A = I$ , $A, B, I \in M_{n} (R)$ has no solution.
Prove that ${a + bi ∣ a, b \in F_{3}}$ has nine elements and is a field.
$A, B$ are $n \times n$ matrices and $A + B = A B$ . then show that $A B = B A$ .
In a town with $n$ people, $m$ clubs have been formed. Every club has odd number of members, and every two clubs have even number of members in common. PT $m \leq n$ .
SMMC 2023 pB 3