Let be matrices such that , where is the identity matrix. Which of the following is always true?

is non-singular Explanation: Solving: Equation: Taking common from left: Condition for Non-Singular: If , then and Since , is hamesha non-singular hoga. Sahi Option: (b) is non-singular

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IGDTUW 2025 Mathematics PYQ — Let be matrices such that , where is the identity matrix. Which o… | Mathem Solvex

A.
$A$ is non-singular
B.
$B$ is non-singular
(Correct Answer)
C.
$A + B$ is non-singular
D.
$AB$ is non-singular

Correct Answer:

$B$ is non-singular

Explanation

Solving:

Equation: $BA + B^2 + BA^2 = I$
Taking $B$ common from left: $B(A + B + A^2) = I$
Condition for Non-Singular:

If $X \cdot Y = I$ , then $|X| \cdot |Y| = |I| = 1$

$\implies |B| \neq 0$ and $|A + B + A^2| \neq 0$

Since $|B| \neq 0$ , $B$ is hamesha non-singular hoga.

Sahi Option: (b) $B$ is non-singular

IGDTUW 2025 — Mathematics PYQ

Choose the correct answer:

Explanation

Explanation