Matrices

Q1.For the matrix A = [[1,1],[0,1]], A^n equals:

• A[[1,n],[0,1]]
• B[[n,n],[0,n]]
• C[[1,1],[0,n]]
• D[[n,1],[0,1]]

Q2.If A is a skew-symmetric matrix of order n, then Aⁿ (n odd) is:

• ASymmetric
• BSkew-symmetric
• CZero matrix
• DIdentity matrix

Q3.Let A be a 2×2 matrix. Which of the following is NOT always true?

• AA + A' is symmetric
• BA – A' is skew-symmetric
• CAB = BA
• D(A')' = A

Q4.If A = [[2, –1],[–1, 2]] and f(A) = A² – 4A + 3I, then f(A) equals:

• A[[–1,0],[0,–1]]
• B[[0,1],[1,0]]
• C[[0,0],[0,0]]
• D[[3,0],[0,3]]

Q5.Given A = [[1,2],[3,4]] and B = [[5,6],[7,8]], the (1,2) element of 2A – 3B is:

• A–14
• B–14
• C–18
• D14