Algebra Matrices Mock Tests

Let S = {x ∈ ℤ : −1 ≤ x ≤ 1}. The number of 3 × 3 matrices with entries from S such that the sum of each row equals the sum of the corresponding column (i.e., R_i = C_i for i = 1, 2, 3) is:

Let A be a 3x3 matrix. If A can be expressed as the sum of a symmetric matrix S and a skew-symmetric matrix T, then:

Let A be a 3x3 matrix with eigenvalues 1, 2, and 3. Which of the following is/are TRUE?

The number of 3 x 3 symmetric matrices with entries from {0, 1} is:

Let A be a 2x2 matrix satisfying A² - 4A + I = O. If tr(A) = 4, then det(A) equals:

Let S be the set of all 2×2 matrices [[a,b],[c,d]] with a, b, c, d ∈ {0, 1, 2, ..., 9} such that a + b = 5, c + d = 5, a + c = 5, and b + d = 5. The number of matrices in S is

Let S be the set of all 3 × 3 matrices with entries from {0, 1, 2} such that the sum of all entries in each row equals 2. The number of such matrices is:

Let S = {1, 2, 3, ..., 10}. The number of 2×2 matrices with distinct entries from S such that the sum of each row equals 5 and the sum of each column equals 5, is