Please tell me the solutions and correct options for these questions:- 14,15,16,17,18,19,20,21,22,23,24,25

iv) a, c, d are correct. L14. 1fA=3 and B-.then L.10. IFA= ,then its inverse is in order that AB = 0, the values of r and y will be respectively i)-6 and-1 ii)-6 and -3 (iv)-5 and -14 (ii) 6 and 1 1.15. If A is a 2 x 2 non-singular square (iv) A*2 Scanned with CamScanner matrix, then adj(adjA) is i) A (i) A (ii) A-l LINEAR ALGEBRA 9 1.4. If A, B are two square matrices such that AB = A and BA = B, then 1.16. If A = (* y 2), B=| ) both A and B are idempotent (i) only A is idempotent ii) only B is idempotent (iv) neither A nor B is idempotent , then (ard + by + cz + 2hxy 1.22. Let A be a non-zero n x n matrix. Then + 2gzr + 21yz) can be expressed as ) (BA) (ii) CAC)B A+A and A- A' are respectively i) skew-symmetric and symmetric (i) symmetric and skew-symmetric (ii) singular and non-singular iv) non-singular and singular (ii) (AB)C (iv) (AB)A 1.17. IfA and B are any two square matrices is equal to of order 2 x 2, then (A + B i) A+2AB + B2 (Gi) A2 +2BA +B2 (ii) A2 + AB- BA + B2 (iv) A + AB + BA + B2 1 2 3 1.23. The rank of the matrix 2 01s lo1 2 1.18. IfA is an invertible matrix whose inverse (i)0 i) 1 i) 3 (iv) 2 1.24. A real (or complex) square matrix can be uniquely expressed as the sum of () a symmetric matrix and a skew- is the matrix then Ais 1/3 SymmetriC matrix (i) two square matrices (ii) two symmetric matrices iv) two skew-symmetric matrices (i5 1/6 5/2 -3/2 /s 1/6) /4) 1.25. Let A and B be two square matrices of same order. Then AB = O implies that (i) either A = O or B =O or both A and 1.19. Let A = (4n xn be a nilpotent matrix ot ndex K. Lnen () T,-A is invertible (i) T, +A is nilpotent (in) ,tA is a zero matrix iv)-A js a zero matrix B are singular matrices (ii) both A and B are non-singular (Gii) A is singular and B is non-singular (iv) A is non-singular and B is singular 1.26. A square matrix A in which the element o.The matrix CoS 6sin 6 -sin cos 0) aj=0 for i>jis called (i) diagonal matrix (ii) lower triangular matrix is symmetric (ii) skew-symmetric n) orthogonal (iv) singular