Part BCSIR NET June 2025rank-exactly-one-excludes-the-zero-matrix-and-is-not-the-invertible-count

Rank exactly one excludes the zero matrix and is not the invertible count

Let 𝔽 $_{5}$ denote the field with 5 elements. How many 2 × 2 matrices with entries in 𝔽 $_{5}$ have rank one?

A.125
B.144✓
C.145
D.480

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Rank exactly one excludes the zero matrix and is not the invertible count

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