If \( A=\begin{bmatrix}2 & 3\\ 1 & 2\end{bmatrix} \) satisfies the equation \( A^{2}-KA+I=O \), then the value of K is (Where I is an identity matrix of order 2)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4
By the Cayley-Hamilton theorem, every 2 × 2 matrix satisfies
\( \displaystyle A^{2}-(\mathrm{tr}\,A)\,A+|A|\,I=O \)
Here \( \mathrm{tr}\,A=2+2=4 \) and \( |A|=4-3=1 \), so \( A^{2}-4A+I=O \).
Comparing this with \( A^{2}-KA+I=O \) gives \( K=4 \).
NCERT (2026-27 edition):
Inverse of a Matrix
