CBSE Class 12 (Commerce) Matrices — practice questions
67 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Commerce) Matrices in the app →The transpose of $A^T$ is:For matrices A (3×2) and B (2×4), the product AB has order:The transpose of the product (AB)^T equals:Matrix multiplication is:The determinant of the 2×2 matrix [[a, b], [c, d]] equals:A matrix A has an INVERSE if and only if:By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:An ORTHOGONAL matrix A satisfies:The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A is:A matrix is best described as which kind of arrangement of numbers?A matrix with 3 rows and 4 columns has which order?How many entries does a matrix of order 4 × 5 contain?In the notation aij, the subscript j tells the element's:A matrix of order 1 × n is known as a:An m × n matrix is a square matrix when:Another name for a matrix whose elements are all zero is:In a diagonal matrix, each element with i not equal to j is:Which square matrix has 1 on the main diagonal and 0 everywhere else?Two matrices of the same order are equal only if they also have:If [[x, 3], [2, y]] = [[5, 3], [2, 7]], then x + y equals:If [[2x + 1, 4], [0, 3]] = [[9, 4], [0, 3]], the value of x is:A 2 × 3 matrix and a 3 × 2 matrix share the same six entries. They are:The second row of [[1, 2], [3, 4]] + [[5, 6], [7, 8]] is:A zero matrix O of the same order satisfies A + O = A, so O is the additive:By the commutative law of addition, A + B always equals:If A = [[1, -2], [3, 0]], then 3A has first row:For A = [[2, 4], [6, 8]], the matrix (1/2)A is:For scalars k and l, the matrix (k + l)A equals:The rule k(A + B) = kA + kB holds when A and B have:The product AB exists only if the number of columns of A equals:If A is 2 × 3 and B is 3 × 4, the order of AB is:For A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], the product AB is:A row matrix [1 2 3] multiplied by the column with entries 4, 5, 6 gives:If the product AB is a zero matrix, then:The equation (AB)C = A(BC) states which law of multiplication?The identity A(B + C) = AB + AC is called the:For a square matrix A of order n, the product IA with identity I equals:If A = [[2, 0], [0, 3]], then A squared equals:The first row of [[2, 1], [1, 0]] times [[1, 2], [3, 4]] is:The transpose of a matrix is obtained by:If A has order 3 × 5, its transpose has order:Transposing a matrix twice, (A')', gives:For a constant k, the transpose (kA)' equals:Which of these matrices is symmetric?For A = [[1, 2], [4, 3]], the matrix (A + A')/2 has off-diagonal entry:For any square matrix A, the matrix A + A' is always:Any square matrix can be written as the sum of a symmetric matrix and a:A real matrix that is both symmetric and skew symmetric must be the:If B is the inverse of a square matrix A, then:A square matrix that possesses an inverse is called:For invertible matrices A and B of the same order, (AB) inverse equals:The inverse of the matrix [[2, 0], [0, 4]] is:If B is the inverse of A, then the inverse of B is:A matrix has 12 elements. Which order is impossible for it?How many different orders are possible for a matrix with 6 elements?In a 3 × 3 matrix with aij = i + j, the element a23 equals:A 2 × 2 matrix has aij = 2i - j. Its first row is:For the 2 × 2 matrix with aij = i × j, the sum of all elements is:A 3 × 3 diagonal matrix has all diagonal entries nonzero. How many zero entries does it have?A 4 × 4 scalar matrix has k = 5. The sum of all its elements is:If A is skew symmetric and a12 = 7, then a21 equals:For A = [[1, 2], [3, 4]], the diagonal entries of A - 2I add up to:For A = [[2, -1], [1, 0]], the expression A squared - 2A + I equals:For A of order m × n and B of order k × l, both AB and BA exist iff:In a product AB, the number of rows in the result equals the rows of:The difference A - B of two matrices is defined as: