If A = [[i, 0], [0, i]], n∈N, then A^4n equals Watch Solution
If A = [[1, 0, 0], [0, 1, 0], [a, b, -1]], then A^2 is equal to Watch Solution
If A and B are two matrices such that AB = A and BA = B, then B^2 is equal to (a) B (b) A (c) 1 (d) 0 Watch Solution
If AB = A and BA = B, where A and B are square matrices, then Watch Solution
If A and B are two matrices such that AB = B and BA = A, then A^2 + B^2 is equal to (a) 2AB (b) 2BA (c) A + B (d) AB Watch Solution
If [[cos2π/7, -sin2π/7], [sin2π/7, cos2π/7]]^k = [[1, 0], [0, 1]], then the least positive integral value of k is Watch Solution
If the matrix AB is zero, then (a) It is not necessary that either A =O or, B=O (b) A = O or B = O (c) A = O and B = O (d) all the above statements are wrong Watch Solution
Let A = [[a, 0, 0], [0, a, 0], [0, 0, a]], then A^n is equal to Watch Solution
If A, B are square matrices of order, 3, A is non-singular and AB = O, then B is a (a) null matrix (b) singular matrix (c) unit matrix (d) non-singular matrix Watch Solution
If A = [[n, 0, 0], [0, n, 0], [0, 0, n] and B = [[a1, a2, a3], [b1, b2, b3], [c1, c2, c3]], then AB is equal to Watch Solution
If A = [[1, a], [0, 1]], then A^n (where n∈N) equals Watch Solution
If A = [[1, 2, x], [0, 1, 0], [0, 0, 1]] and B = [[1, -2, y], [0, 1, 0], [0, 0, 1]] and AB = I3, then x + y equals Watch Solution
If A = [[1, -1], [2, -1]], B = [[a, 1], [b, -1]] and (A + B)^2 = A^2 + B^2, then values of a and b are Watch Solution
If A = [[α, β], [γ, -α]] is such that A^2 = I, then Watch Solution
If S = sij] is a scalar matrix such that sii = k and A is a square matrix of the same order, then AS = SA = ? (a) Ak (b) k+ A (c) kA (d) ks Watch Solution
If A is a square matrix such that A^2 = A, then (I + A)^3 – 7A is equal to (a) A (b) I – A (c) I (d) 3A Watch Solution
If a matrix A is both symmetric and skew-symmetric, then (a) A is a diagonal matrix (b) A is a zero matrix (c) A is a scalar matrix (d) A is a square matrix Watch Solution
The matrix [[0, 5, -7], [-5, 0, 11], [7, -11, 0]] is (a) a skew-symmetric matrix (b) a symmetric matrix (c) a diagonal matrix (d) an upper triangular matrix Watch Solution
If A is a square matrix, then AA is a (a) skew-symmetric matrix (b) symmetric matrix (c) diagonal matrix (d) none of these Watch Solution
If A and B are symmetric matrices, then ABA is (a) symmetric matrix (b) skew-symmetric matrix (c) diagonal matrix (d) scalar matrix Watch Solution
If A = [[5, x], [y, 0]] and A = A^T, then Watch Solution
If A is 3×4 matrix and B is a matrix such that A^TB and BA^T are both defined. Then, B is of the type (a) 3×4 (b) 3×3 (c) 4×4 (d) 4×3 Watch Solution
If A = [aij] is a square matrix of even order such that aij = i^2 – j^2, then (a) A is a skew-symmetric matrix and |A|= 0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A| = 0 (d) none of these. Watch Solution
If A = [[cos θ, -sin θ], [sin θ, cos θ]], then A^T + A = I2, if Watch Solution
If A = [[2, 0, -3], [4, 3, 1], [-5, 7, 2]] is expressed as the sum of a symmetric and skew-symmetric matrix, the symmetric matrix is Watch Solution
Out of the following matrices, choose that matrix which is a scalar matrix : Watch Solution
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is (a) 27 (b) 18 (c) 81 (d) 512 Watch Solution
Which of the given values of x and y make the following pairs of matrices equal ? [[3x+7, 5], [y+1, 2-3x]] and [[0 ,y-2], [8, 4]] Watch Solution
If A = [[0, 2], [3, -4]] and kA = [[0, 3a], [2b, 24]], then the values of k, a, b are respectively Watch Solution
If I = [[1, 0], [0, 1]], J = [[0, 1], [-1, 0]] and B = [[cos θ, sin θ], [-sin θ, cos θ]], then B equals Watch Solution
The trace of the matrix A = [[1, -5, 7], [0, 7, 9], [11, 8, 9]] is Watch Solution
If A = [aij] is a scalar matrix of order n×n such that aii = k for all i, then trace of A is equal to (a) nk (b) n+k (c) n/k (d) none of these Watch Solution
The matrix A = [[0, 0, 4], [0, 4, 0], [4, 0, 0]] is a (a) square matrix (b) diagonal matrix (c) unit matrix (d) none of these Watch Solution
The number of possible matrices of order 3×3 with each entry 2 or 0 is (a) 9 (b) 27 (c) 81 (d) none of these Watch Solution
If [[2x + y, 4x], [5x – 7, 4x]] = [[7, 7y – 13], [y, x + 6]], then the value of x + y is Watch Solution
If A is a square matrix such that A^2 = I, then (A – I)^3 + (A + I)^3 – 7A is equal to (a) A (b) I – A (c) I + A (d) 3A Watch Solution
If A and B are two matrices of order 3×m and 3×n respectively and m = n, then the order of 5A – 2B is (a) mx3 (b) 3×3 (c) mxn (d) 3xn Watch Solution
If A is a matrix or order m×n and B is a matrix such that AB^T and B^TA are both defined, then the order of matrix B is (a) mxn (b) n×n (c) nxm (d) mxn Watch Solution
If A and B are matrices of the order, then AB^T – B^T A is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix Watch Solution
If matrix A = [aij]2×2, where aij = {1, if i ≠ j 0, if i + j, then A^2 is equal to Watch Solution
If A = 1/π[[sin^1(πx), tan^-1(π/x)], [sin^-1(π/x), cot^-1(πx)]], B = 1/π[[-cot^-1(πx), tan^-1(πx)], [sin^1(π/x), -tan^-1(πx)]], then A-B is equal to Watch Solution
If A and B are square matrices of the same order, then (A + B)(A – B) is equal to (a) A^2 – B^2 (b) A^2 – BA – AB – B^2 (c) A^2 – B^2 + BA – AB (d) A^2 – BA + B^2 + AB Watch Solution
If A = [[2, -1, 3], [-4, 5, 1]] and B = [[2, 3], [4, -2], [1, 5]], then (a) only AB is defined (b) only BA is defined (c) AB and BA both are defined (d) AB and BA both are not defined Watch Solution
The matrix A = [[0, -5, 8], [5, 0, 12], [-8, -12, 0]] is a (a) diagonal matrix (b) symmetric matrix (c) skew-symmetric matrix (d) scalar matrix Watch Solution
The matrix A = [[1, 0, 0], [0, 2, 0], [0, 0, 4]] is (a) identity matrix (b) symmetric matrix (c) skew-symmetric matrix (d) diagonal matrix Watch Solution
