JEE Main 2025 — Matrices Questions with Solutions

Let A= [ai j ] be 3 × 3 matrix such that A [arrayl0 \ 1 \ 0array ]= [arrayl0 \ 0 \ 1array ], A [arrayl4 \ 1 \ 3array ]=…

Let A be a 3 × 3 matrix such that $\begin{aligned} & |\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{…

Let M denote the set of all real matrices of order 3 × 3 and let S=\-3,-2,-1,1,2\. Let aligned & S₁= \A= [aij ] M: A=AT…

Let α be a solution of x²+x+1=0, and for some a and b in R, [arraylll4 & a & barray ] [arrayccc1 & 16 & 13 \ -1 & -1 &…

Let A be a 3 × 3 matrix such that X^T A X=O for all nonzero 3 × 1 matrices X= [arraylx \ y \ zarray ]. If A [arrayl1 \…

Let a R and A be a matrix of order 3 × 3 such that det(A)=-4 and A+I= [arraylll1 & a & 1 \ 2 & 1 & 0 \ a & 1 & 2array ]…

If A, B, and (adj (A⁻¹ )+adj (B⁻¹ ) ) are non-singular matrices of same order, then the inverse of A (adj (A⁻¹ )+adj (B…

The number of singular matrices of order 2 , whose elements are from the set \2,3,6,9\ is

Let A= [arraycc1√(2) & -2 \ 0 & 1array ] and P= [arraycc θ & - θ \ θ & θarray ], θ0. If B=PAPT, C=PT B¹⁰ P and the sum…

Let A be a matrix of order 3 × 3 and |A|=5. If |2 adj(3 ~A adj(2 ~A))|=2^α · 3^β · 5^γ α, β, γ N then α+β+γ is equal to