Matrices Test -...

The sum and product of matrices A and B exist. Which of the following implications are necessarily true?

I. A and B are square matrices of same order.

II. A and B are non-singular matrices.

Select the correct answer using the code give below.

If AB^T is defined as a square matrix then what is the order of the matrix B, where matrix A has order 2 × 3.

If \(A = \left[ {\begin{array}{*{20}{c}} {\cos 2θ }&{ - \sin 2θ }\\ {\sin 2θ }&{\cos 2θ } \end{array}} \right]\) and A + A^T = I

Where I is the unit matrix of 2 × 2 & A^T is the transpose of A, then the value of θ is equal to

From the matrix equation AB = AC, where A, B, C are the square matrices of same order, we can conclude B = C provided

If \( A =\begin{bmatrix} 1 & 2 \\\ 3 & 4 \end{bmatrix} \) and \(B =\begin{bmatrix} a & 0 \\\ 0 & b \end{bmatrix}\), where a, b and natural numbers, then which one of the following is correct ?

Consider two matrices M₁ and M₂ with M₁*M₂ = 0 and M₁ is non singular. Then which of the following is true?

If A is a square matrix such that A² = I, then A³ + (A + I)² - 9A - I2 - A2 is

For matrices of the same dimension M, N, and scalar c, which one of these properties DOES NOT ALWAYS hold?

If \(A = \left[ {\begin{array}{*{20}{c}} 2&3\\ { - \;1}&2 \end{array}} \right] = \frac{1}{2}\;\left( {P + Q} \right)\) where P is symmetric and Q is skew symmetric matrix then P and Q are ?

If A, B, C are square matrices of the same order, then which of the following is true?