Mark each statement T if the statement is always true or F if it's ever false. All A, B, C, and D are matrices, and I is the identity matrix. Do not assume anything beyond what is explicitly stated. (a) If A and B are m × n matrices, then both products AB™ and A™B are defined. (b) If C = D, then BC = BD. %3D (c) If BC = BD, then C = D. (d) Every square matrix is the product of elementary matrices. (e) If AB = I, then A is invertible. (f) For any A, det(-A) = – det A. (g) If A and B are square matrices with det A = 2 and det B = 3, then det(A + B) = 5. (h) If two rows of a square matrix A are the same, then det A = 0. (i) If det A = 5, then A is invertible and det(A¯') =. (j) If A² = 0, then A is singular.

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…