Properties of Determinants: JEE Questions & Solutions

If A = bmatrix 2 & 3 3 & 5 bmatrix, then the determinant of the matrix A^2025 - 3A^2024 + A^2023 is

Let |A| = 6, where A is a 3 3 matrix. If | adj( adj(A^2 adj(2A)))| = 2^m 3^n, then m + n is equal to:

Let f(x)= 7x^10+9x^8(1+x^2+2x^9)^2 dx, x0, and A= bmatrix 0 & 0 & 1 14 & f'(1) & 1 & 4 & 1 bmatrix. If B= adj( adj A), then the value of…

Let A be a square matrix of order 3 such that (A) = -2 and (3 adj(-6 adj(3A))) = 2^m+n 3^mn, where m n. Then 4m + 2n is equal to:

Let A = [ aij ] = [ arraycc 5 128 & 4 5 5 8 & 4 25 array ]. If Aij is the cofactor of aij, Cij = k=1^2 aik Ajk, and C = [Cij], then 8|C| is…

Let A R be a matrix of order 3 3 such that (A) = -4 and A + I = [ arrayccc 1 & 1 & 1 2 & 0 & 1 4 & 1 & 2 array ] where I is the identity…

If A = bmatrix 2 & 1 -1 & 2 bmatrix, B = bmatrix 1 & 0 0 & 1 bmatrix, C = ABA^T, and X = A^T C^2 A, then (X) is equal to:

Let A be a 3 3 matrix such that |adj(adj(A))| = 12^4. Then |A^-1adj(A)| is equal to:

Let f(x) = bmatrix 1 + ^2 x & ^2 x & 2x ^2 x & 1 + ^2 x & 2x ^2 x & ^2 x & 1 + 2x bmatrix where x [ 6, 3 ]. If, are respectively the…

If A is a 3 3 matrix and |A| = 2, then |3 adj(|3A|A^2)| is equal to: