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Matrices & Determinants (Foundations)

Core skills for this exam family.

Phase 2 · JEE

FoundationsStandardAdvanced

Matrices & Determinants: core idea

det⁡(abcd)=ad−bc\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bc.

Example problem: hint and answer

det⁡(1234)\det\begin{pmatrix}1&2\\3&4\end{pmatrix}?

Hint: ad−bcad-bc. Answer: -2.

Practice (9 problems — type your answers)

  • 1. Trace of (2005)\begin{pmatrix}2&0\\0&5\end{pmatrix}?

  • 2. Det of I2I_2?

  • 3. Transpose of (12)\begin{pmatrix}1&2\end{pmatrix} has how many rows?

  • 4. 2(1001)2\begin{pmatrix}1&0\\0&1\end{pmatrix}: det?

  • 5. Size of 2×32\times3 times 3×43\times4 product: rows?

  • 6. Det (5003)\begin{pmatrix}5&0\\0&3\end{pmatrix}?

  • 7. Inverse of II: det?

  • 8. Zero matrix 2×22\times2 det?

  • 9. If A=(1000)A=\begin{pmatrix}1&0\\0&0\end{pmatrix}, rank?

Matrices & Determinants Practice Problems — Foundations