If A is a square matrix such that A2=A and I is the identity matrix of same order as A, then the matrix (2I+A)3−19A−3I is equal to
Held on 15 May 2025 · Verified 13 Jul 2026.
5I
5A
7I
7A
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If f(x) = 2x + 3, then f⁻¹(x) is:
Consider a L.P.P, Maximize $Z = 3x + 5y$ subject to constraints $2x + 6y ≤ 6$, $x - y ≥ 0$, $x ≥ 0$, $y ≥ 0$. Then which of the following are true? (A) The feasible region of L.P.P is bounded region (B) The corner points of the feasible region are (0, 0), (2, 2), (0, 1) (C) Maximum value of Z is 9 (D) Point (1, 3) lies in the feasible region Choose the correct answer from the options given below:
If A and B are square matrices of order 3 such that |A| = -1 and |B| = 5, then the value of |3AB| is
Let $AX = B$ be a system of three linear equations in three variables. Then the system has (A) a unique solutions if $|A| = 0$ (B) a unique solutions if $|A| \neq 0$ (C) no solutions if $|A| = 0$ and (adj A) $B \neq 0$ (D) infinitely many solutions if $|A| = 0$ and (adj A)$B = 0$ Choose the correct answer from the options given below:
Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true? (A) AB = BA (B) (AB)⁻¹ = B⁻¹ A⁻¹ (C) $(AB)^T = B^T A^T$ (D) AB = 0 ⇒ A = 0 or B = 0 Choose the correct answer from the options given below:
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